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SB    35    Mfi3 


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A  MECHANICAL  THEORY 


OF   THE 


*-, 


SOLAE    COEOKA.  : 


BY  J.  M/SCHAEBERLE. 

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SACRAMENTO: 

STATE    OFFICE,    :    :    :    A.    J.    JOHNSTON,    SUPT.    STATE    PRINTING. 

1891. 


I'late  VII. 


Models  illustrating  the  method, of" fdhn£tlorfol  the 

Polar  Ray<3.!  ;\\i 


A  MECHANICAL  THEORY 


OF   THE 


SOLAE    COKONA. 


BY  J.  M.  SCHAEBERLE. 
H 


SACRAMENTO: 

STATE  OFFICE,    :   :    A.    J.    JOHNSTON,    SUPT.    STATE   PRINTING. 

1891. 


S4- 


A  MECHANICAL  THEORY  OF  HfE  < 3Q.LAK 

By   J.    M.    SCHAEBERLE. 


The  essential  principles  which  lie  at  the  foundation  of  the 
theory  here  advanced  were  first  published  last  spring  in  a  short 
note  entitled  "A  Mechanical  Theory  of  the  Solar  Corona." 
(Publications,  A.  S.  P.,  No,  7;  Mon.  Not.,  R.  A.  S.,  Vol.  4,  p. 
372.)  One  year  previous  to  this  time  (in  February,  1889),  I 
expressed  my  belief  to  Professor  HOLDEN  and  other  astrono- 
mers at  this  Observatory,  that  the  coronal  form  was  produced 
by  streams  of  matter  ejected  from  the  lower  latitudes  of  the 
Sun.  At  the  time  Professor  HOLDEN  desired  me  to  work  up  the 
subject,  and  offered  to  give  me  any  assistance  in  his  power; 
but  as  I  had  not  given  much  attention  to  solar  observation, 
and  was  still  less  familiar  with  the  physical  researches  of  those 
who  made  the  Sun  a  special  study,  I  did  not  deem  the  subject 
a  proper  one  for  me  to  cope  with  at  that  time,  although  I 
intended  to  attack  the  problem  later  on. 

Through  the  liberality  of  Colonel  CROCKER,  who  offered  to 
bear  the  expense  of  an  expedition  to  South  America,  to  observe 
the  solar  eclipse  of  December  21-22,  this  problem  of  the  solar 
corona  was  to  rivet  my  attention  sooner  than  I  had  anticipated. 

The  highly  satisfactory  results  secured  by  the  Lick  Observa- 
tory party,  consisting  of  S.  W.  BURNHAM  and  J.  M.  SCHAEBERLE, 
at  Cayenne,  South  America,  were  such  that  after  the  develop- 
ment of  our  plates  the  views  which  I  had  held  for  nearly  a  year 
were  very  much  strengthened. 

By  the  time  we  again  reached  the  Lick  Observatory  the  super- 
structure of  the  present  theory  was  built,  and  it  only  required 
the  finishing  touches  relating  to  the  more  minute  details  of  the 
corona,  and  a  comparison  with  published  observations,  to  bring 
the  matter  to  its  present  shape. 

In  what  follows  I  shall  present  the  theoretical  investigations 
in  as  simple  and  brief  a  manner  as  possible. 

736351 


2         A  Mechanical  Theory  of  the  Solar  Corona, 

$ 

Three  well  known  facts  serve  as  a  basis  on  which  the  whole 
theory  rests.     They  are: 

1.     The  eruptions  of  the  Sun's  surface  are  most  active  and 


.'    The  Sun  'rotates,  apout  an  axis  passing  through  its  center. 
\  ;  &<  \Ti$i$aZis  i\  Helped  to  the  plane  of  the  Earth's  orbit  at  an 
angle  of  about  82%°. 

As  the  present  theory  also  enables  one  to  reproduce,  graph- 
ically, practically  all  the  phenomena  observed  during  a  total 
eclipse  of  the  Sun,  and  as  the  graphical  construction  is  in  strict 
accordance  with  known  mechanical  laws,  the  following  brief 
statement  of  the  theory  may  be  properly  made  here: 

The  theoretical  corona  is  caused  by  light  emitted  and  reflected 
from  streams  of  matter  ejected  from  the  Sun,  by  forces  which,  in 
general,  act  along  lines  normal  to  the  surface  of  the  Sun  ;  these 
forces  are  most  active  near  the  center  of  each  Sun-spot  zone. 

Owing  to  the  rotation  of  the  Sun,  the  streams  of  matter  will 
not  lie  along  normals,  since  the  angular  velocity  of  different 
portions  of  a  stream  grows  less  as  the  distance  from  the  Sun 
increases;  in  other  words,  the  streams  are  of  double  curvature. 
Each  individual  particle  of  the  stream,  however,  describes  a 
portion  of  a  conic  section,  which  is  a  very  elongated  ellipse,  so 
long  as  the  initial  velocity  is  less  than  three  hundred  and 
eighty-three  miles  per  second  (assuming  that  the  Sun's  atmos- 
phere, as  shown  by  various  observations,  is  exceedingly  rare). 

Certain  variations  in  the  type  of  the  corona  admit  of  an  ex- 
ceedingly simple  explanation,  being  principally  due  to  the 
change  in  the  position  of  the  observer  with  reference  to  the 
plane  of  the  Sun's  equator.  According  as  the  observer  is  above, 
below,  or  in  the  plane  of  the  Sun's  equator,  the  perspective  over- 
lapping and  interlacing  of  the  streamers  cause  the  observed 
apparent  variations  in  the  type  of  the  corona. 

The  general  direction  in  which  these  ejective  forces  act  will 
be  along  radii.  There  may,  of  course,  be  numerous  particular 
exceptions  to  this  general  direction. 

Similarly,  since  observation  shows  that  certain  solar  motions 
are  apparently  confined  to  special  regions,  which  are  symmet- 
rically situated  with  reference  to  the  axis  of  rotation  of  the  Sun, 
we  are  evidently  justified  in  assuming  that  the  forces  which 
cause  these  motions  are,  in  general,  uniformly  distributed 


By  J.  M.  Schaeberle.  3 

around  each  circle  of  latitude,  since  there  is  no  a  priori  reason 
why,  in  a  highly  heated  rotating  mass  of  matter,  the  solar  ac- 
tivity should  be  confined  to  any  particular  circles  of  longitude. 
There  may,  of  course,  be  particular  exceptions  to  a  uniform  dis- 
tribution of  the  forces. 

As  the  exact  nature  of  the  atmosphere  surrounding  the  Sun 
is  unknown,  and  as  its  extreme  rarity  has  been  demonstrated 
by  various  observations,*  the  heliocentric  motions  of  all  parti- 
cles exterior  to  the  Sun's  visible  surface  will  be  considered  to 
be  unimpeded  by  solar  atmospheric  resistances. 

What  precedes  may  be  taken  to  be  a  complete  statement  of 
the  general  features  of  the  mechanical  theory  of  the  corona. 
In  order  to  compare  it  with  observation  it  will  be  necessary  to 

*NOTES. — With  reference  to  the  views  of  solar  physicists  on  the  subject  of  the 
Sun's  atmosphere,  I  quote  a  few  paragraphs  giving  the  most  recent  conclu- 
sions : 

Professor  YOUNG,  in  his  General  Astronomy,  says:  "The  corona  cannot  be  a 
true  '  solar  atmosphere '  in  any  strict  sense  of  the  word.  No  gaseous  envelope 
in  any  way  analogous  to  the  earth's  atmosphere  could  possibly  exist  there  in 
gravitational  equilibrium  under  the  solar  conditions  of  pressure  and  tempera- 
ture. The  corona  is  probably  a  phenomenon  due  somehow  to  the  intense 
activity  of  the  forces  there  at  work;  meteoric  matter,  cometic  matter,  matter 
ejected  from  the  Sun,  are  all  concerned. 

"  That  this  matter  is  inconceivably  rare  is  evident  from  the  fact  that  in  sev- 
eral cases  comets  have  passed  directly  through  the  corona  without  experiencing 
the  least  perceptible  disturbance  of  their  motions.  It  is  altogether  probable 
that  at  a  very  few  thousand  miles  above  the  Sun's  surface,  its  density  becomes 
far  less  than  that  of  the  best  vacuum  we  can  make  in  an  electric  lamp." 

The  following  paragraphs  are  from  Mr.  KEELER'S  Report  on  the  Solar  Eclipse 
of  January  1, 1889  (published  by  the  Lick  Observatory): 

"  Spectroscopic  observation  furnishes  us  with  many  facts  which  cannot  be 
reconciled  with  the  theory  of  an  extensive  solar  atmosphere.  Two  of  the  most 
important  objections  drawn  from  this  source  are  given  below;  the  first  has 
long  been  recognized  as  especially  perplexing: 

"  (1)  The  pressure  at  the  surface  of  the  chromosphere  is  shown  by  the  spec- 
troscope not  to  exceed  that  of  a  few  millimetres  of  mercury,  and  this  we  must 
accept  as  the  pressure  due  to  an  atmosphere  from  half  a  million  to  a  million 
of  miles  deep,  notwithstanding  the  fact  that  the  force  of  gravity  is  twenty- 
seven  times  as  great  at  the  surface  of  the  Sun  as  at  the  surface  of  the  Earth. 

"(2)  According  to  theory,  as  well  as  observation,  the  upper  limits  of  the 
gaseous  envelopes  of  the  Sun  ought  to  be  ordered  according  to  their  densities. 
The  material  which  produces  the  1474  K  line,  and  which  may  always  be  seen 
in  the  chromosphere  spectrum,  is,  according  to  this  criterion,  as  unmistakably 
denser  than  hydrogen  as  is  magnesium  vapor  or  iron  vapor;  but  if  we  accept 
the  coronal  spectrum  as  evidence  of  the  existence  of  an  atmosphere,  we  are, 
by  exactly  the  same  principle,  driven  to  the  same  conclusion  that  the  1474  K 
material  is  far  less  dense  than  hydrogen.  The  contradiction  could  not  be 
more  abrupt  and  inexplicable."— HASTINGS. 
9  s 


4         A  Mechanical  Theory  of  the  Solar  Corona, 

deduce  the  laws  which  govern  the  appearances  of  a  typical 
corona  produced  by  solar  eruptions  of  the  character  already  de- 
scribed. For  convenience,  I  have  made  no  distinction  between 
the  real  and  these  theoretical  solar  phenomena;  it  should 
therefore  be  borne  in  mind  that  in  the  discussion  for  deducing 
the  laws  of  coronal  phenomena  this  theoretical  corona  is  always 
the  one  referred  to. 

We  shall  first  inquire  into  the  form  of  the  trajectory  of  a 
particle  ejected  from  the  Sun  by  a  force  sufficient  to  remove  it 
one  or  more  diameters  from  the  Sun's  surface. 

If  there  were  no  motion  of  rotation,  all  particles  ejected  from 
a  given  point  on  the  Sun's  surface  would,  in  general,  lie  along  a 
normal  passing  through  this  point.  The  rotation  of  the  Sun, 
however,  introduces  other  forces,  the  resultant  of  which  can, 
without  appreciable  error,  be  regarded  as  acting  at  right  angles 
to  both  the  axis  of  rotation  and  the  line  along  which  the 
ejective  force  acts. 

In  considering  the  motion  of  an  ejected  particle: 

Let  T0  denote  the  time  of  one  rotation  of  the  Sun  (in  latitude  <p). 
Let  #0  denote  the  radius  of  the  Sun. 

Let  R   denote  the  radius-vector  of  the  ejected  particle  at  the  time  t. 
Let  ff>  denote  the  heliocentric  latitude  of  the  point  of  ejection. 
Let  v:  denote  the  linear  velocity  of  the  particle  due  to  the  Sun's  rotation. 
Let  v2  denote  the  velocity  of  ejection. 
Let  V  denote  the  resultant  initial  velocity  of  the  particle. 
Let  ^    denote  the  angle  between  a  normal  at  the  point  of  ejection  and  the 
actual  initial  direction  of  motion. 

The  following  expressions  give  the  relations  existing  between 
the  quantities  which  determine  the  subsequent  motion: 


If  T0  is  expressed  in  seconds,  vl  is  the  distance  described  in 
one  second  of  time. 


v\  (2) 

l  (3) 

It  is  evident  that  so  long  as  the  line  of  action  of  the  ejective 
force  is  along  a  normal,  any  transverse  force,  however  great  or 
small,  will  at  once  determine  the  position  of  the  plane  in  which 


By  J.  M.  Schaeberle. 


the  subsequent  motion  of  the  particle  lies,  since  the  lines  of 
action  of  both  forces  must  lie  in  this  plane.  If  there  are  sev- 
eral transverse  forces,  the  plane  of  motion  must  contain  a 
normal  through  the  point  of  ejection  and  the  resultant  of  the 
several  transverse  forces. 

The  value  of  v  x  is  dependent  only  on  q>,  and  can  therefore  be 
determined  accurately.  If  we  assign  different  values  to  v2  we 
can  evidently  compute  all  the  elements  of  the  several  orbits 
which  would  be  described  corresponding  to  different  initial 
velocities,  since  we  also  know  the  mass  and  radius  of  the  Sun. 
In  other  words,  we  have  given  the  radius-  vector  and  the  veloc- 
ity and  direction  of  motion  of  a  particle  at  a  given  instant  of 
time  to  find  all  the  elements  of  the  orbit  described,  the  central 
force  being  known. 

Let  a  denote  the  semi-major  axis  of  the  eclipse  described. 
Let  X2  denote  the  mass  of  the  Sun. 

(The  value  of  K'2  is  such  that  if  the  Sun  acts  on  a  stationary 
material  particle  free  to  move,  at  a  distance  equal  to  the  Earth's 
mean  distance  from  the  Sun,  the  velocity  of  the  particle  at  the 

end  of  one  second  of  time  will  be  equal  to  24x60x60  ) 
The  general  equation  for  undisturbed  motion  is: 


From  which  we  can  evidently  find  a. 

We  next  obtain  the  periodic  time  t  from  the  familiar  expres- 
sion: 

*==-£[-  (5) 

The  eccentricity  s  can  be  found  as  follows: 

Let  R  and  R'  denote  the  distances  of  the  particle  from  the 
two  foci  of  the  eclipse,  then  for  R  —  R0  the  angle  included  be- 
tween R  and  R  is  always  equal  to  180  —  2^,  so  that  we  can  at 
once  write: 

s  =  V  R02  +  R2  —  2  R0  R  cos  (180°  —  2  #)  (6) 

from  which  s  is  readily  found. 

To  determine  the  inclination  of  the  plane  of  the  orbit  to  the 
Sun's  equator,  we  have  given  a  point  (the  Sun's  center)  and  a 
line  (the  actual  path  of  the  particle  —  the  projection  of  this  path 
on  the  Sun's  surface  at  the  instant  of  ejection  being  nearly  parallel 
to  the  equator)  through  which  the  plane  of  the  orbit  must  pass. 


A  Mechanical  Theory  of  the  Solar  Corona, 


The  inclination  of  the  plane  must  evidently  always  be  nearly 

the  same  as  the  latitude  of  the  point  where  the  particle  is  ejected. 

I  have  computed  the  paths  of  particles  for  different  velocities 

of  ejection  in  a  mean  latitude  of  15°.     The  elements  are  given 

in  the  following  table: 

TABLE  I. 


Initial  Velocity 
of  an  Ejected 
Particle=V. 

Angle    between 
the  Normal  at 
the    Point    of 

Semi-Major  Axis 
of  the  Orbit=« 

Periodic     Time 
of    the    Parti- 
cle—if 

£ 

Ejection    and 

Miles  per  second. 

the  Initial  Di- 
rection of  Mo- 
tion;^. 

Radius  of  Sun=l 

Expressed   in 
Days. 

Eccentricity. 

219.1 

0°.318 

0.75 

0.075 

0.9933 

269.2 

.259 

1.00 

.116 

.9950 

311.3 

.225 

1.50 

.214 

.9967 

330.3 

.212 

2.00 

.329 

.9975 

348.3 

.201 

3.00 

.604 

.9983 

357.0 

.196 

4.00 

.930 

.9987 

362.1 

.193 

5.00 

1.300 

.9989 

372.2 

.188 

10.00 

3.678 

.9995 

377.0 

.185 

20.00 

8.263 

.9997 

379.5 

.185 

40.00 

29.42 

.999+ 

379.7 

.185 

80.00 

83.22 

.999+ 

382.0 

.184 

Infinity 

Infinity 

1.000 

Apparent  motions  corresponding  to  component  velocities  of 
two  hundred  and  fifty  miles  per  second  (the  actual  velocity  is, 
as  a  rule,  always  greater  than  the  observed)  are  not  infre- 
quently observed  in  solar  protuberances.  (See  Young's  General 
Astronomy,  page  208.)  It  does  not,  however,  follow  that  the 
forces  producing  these  motions  must  be  correspondingly  great, 
for  if: 


(in  which  F,  V,  and  M  are  respectively  the  moving  force,  the 
maximum  velocity  generated,  and  the  mass  moved),  then  for  a 
constant  force  F  the  velocity  V  will  increase  as  the  mass  M 
diminishes,  and  as  the  resistance  to  motion  is  to  be  considered 
zero,  the  volume  corresponding  to  a  given  mass  may  be  either 
great  or  small  without  affecting  the  velocity. 

The  above  elements  show  that  the  theoretical  orbit  will 
always  be  a  very  elongated  ellipse,  the  perihelion  point  being 
near  the  Sun's  center  and  having  a  longitude  nearly  180°  dif- 
ferent from  the  longitude  of  the  point  of  ejection,  while  the 
nodal  points  will  always  be  90°  and  270°  from  the  theoretical 
perihelion,  and  within  less  than  a  score  of  miles  of  the  Sun's 
center. 


By  J.  M.  Schaeberle. 


Let  us  now  consider  the  circumstances  of  motion  of  a  series  of 
particles  ejected  from  the  same  point  on  the  Sun's  surface  following 
each  other  so  as  to  form  a  continuous  stream.  The  angular  velocity 
of  each  particle  as  it  leaves  the  Sun's  surface  will  be  the  same 
as  that  of  the  Sun,  but  as  the  radius-vector  of  the  particle 
increases  the  angular  velocity  decreases  according  to  rigorous 
mechanical  laws.  Therefore,  while  each  particle  may  be  con- 
sidered as  describing  an  independent  orbit,  the  curve  formed 
by  the  stream  will  not  be  a  conic  section,  but  a  helix,  which, 
so  long  as  the  latitude  of  the  base  of  the  stream  is  not  zero, 
will  necessarily  be  of  double  curvature.  As  all  the  particles 
causing  the  visible  coronal  outlines  are  within  a  few  diameters 
of  the  Sun,  we  can,  without  appreciable  error,  consider  a  given 
stream  as  lying  in  one  plane.  For  simplicity  in  the  discussion, 
a  parabolic  velocity  will  be  assumed  for  all  streams: 

Let  &)o  denote  the  true  anomaly  for  a  radius-vector  7?0  and  time  to. 

Let  &>  denote  the  trae  anomaly  for  a  radius- vector  R  and  time  t. 

Let  T  denote  time  of  the  theoretical  perihelion  passage. 

Let  t  denote  the  time  corresponding  to  R  and  GO. 

Let  0  denote  the  angle  turned  through  by  the  Sun  during  the  time  (t— to). 

With  the  well  known  relations  which  exist  between  (t — T )  and 
oo  in  the  case  of  parabolic  motion,  the  results  given  below  are 
readily  obtained.  The  angle  6  is  zero  at  the  instant  t0  when 
GO  =  GOO  and  R  =  R0.  Both  6  and  GO — GOO  are  measured  from  the 
fixed  heliocentric  direction  in  space  which  the  origin  of  the 
stream  has  at  the  instant  «0.  The  angle  which  a  line  drawn 
from  the  base  of  the  stream  to  any  point  in  the  stream  makes 
with  a  normal  through  this  base,  will  be  called  /. 

TABLE  II. 


Radius-Vector   of 
the  Particle=-ff= 

1.0. 

2.0. 

3.0. 

4.0. 

5.0. 

6.0. 

180°—  oo 

0°  22M 

0°  15'.  6 

0°  12'.  8 

o°  ir.o 

0°  9'.9 

(yy.o 

t—T 

Od.009 

Od.025 

Oi.045 

l^.OTO 

Od.097 

(H.128 

t  —  10 

Od.OOO 

Od.016 

Od.036 

Od.061 

Od.088 

Od.119 

&)  —  a?0  .  

O'.O 

6'.5 

V.S 

ll'.l 

12'.  2 

13M 

0  

o°.o 

0°.2 

0°.5 

0°.8 

1°.2 

1°.6 

J  

0°.2 

0°.5 

0°.9 

1°.3 

1°.8 

8          A  Mechanical  Theory  of  the  Solar  Corona, 


TABLE  II — Continued. 


Radius-  Vector  of  the  Parti  - 

016=^2= 

7.0. 

8.0. 

10.0. 

20.0. 

40.0. 

180°—  GO 

0°  8'.3 

0°  7'.  8 

0°  7'.0 

0°  4'.  9 

0°  3'  5 

t—T 

Od.162 

0*  198 

Od.278 

Od.782 

2d  18 

t—t0  ._. 

Od.153 

Od.189 

Od.269 

Od.773 

2d.17 

G)  —  (i30  _. 

13'.  7 

14'.3 

15'.1 

17'.2 

18'.6 

e 

2°  1 

2°  6 

2°.3 

2°.  8 

The  equation  which  fairly  represents  the  relation  between  R 
and  /,  I  find  to  be  the  following: 

I  =  j,IF  +  tX-l,  (7) 

/  being  expressed  in  degrees  of  arc  and  the  unit  of  R  being  a 
radius  of  the  Sun. 

For  discussing  the  curve  represented  by  the  above  equation, 
it  will  be  more  convenient  to  take  the  origin  on  the  Sun's  sur- 
face at  the  base  of  the  stream  and  refer  the  curve  to  a  normal 
through  this  origin. 

For  all  points  in  any  stream  visible  during  an  eclipse  we  can 
without  sensible  error  write: 

P  =  R  —  1,  (8) 

p  being  the  distance  from  any  point  in  the  stream  to  the  Sun's 
surface. 

Equation  (7)  now  becomes 

f='*(P +  !)'  +  *  A  (9). 

Since  for  our  limits  the  angle  I  will  always  be  small,  the  in- 
clination r  of  the  curve,  at  any  point,  to  a  normal  through  the 
origin  will  be  given  by  the  differential  expression 

^  =  Pgj5-+J=*p(p-fl)+tP  +  I,  (10) 

P  being  expressed  in  degrees  of  arc. 

With  the  aid  of  this  equation  we  obtain  the  following  incli- 
nations P  for  the  corresponding  values  of  p,  the  values  of  / 
being  taken  from  Table  II: 


By  J.  M.  Schaeberle. 


TABLE  III. 


1.0 

0°.5 

2.0 

1.2 

3.0 

.      2.0 

4.0 

3.0 

5.0 

4.1 

6.0 

5.4 

7.0 

6.8 

If  ft  denotes  the  Earth's  angular  distance  above  or  below  the 
plane  of  the  Sun's  equator  at  the  time  of  observation,  a  streamer 
in  latitude  <p,  in  order  to  be  just  visible  at  either  pole  of  the  Sun, 
must  have  a  length  p0  given  by  the  equation: 


Po= 


sn    c± 


— 1 


(11) 


The  values  of  p0  for  the  two  latitudes  15°  and  30°,  and  for 
particular  values  of  ^,  are  given  in  the  following  table  (re- 
ferred to  the  nearer  hemisphere) : 


TABLE  IV. 


Latitude  on  the  ©=<p. 

Angular    Distance   of   the 
Earth  above  the  Plane  of 
the  0's  Equator  =/?. 

Length  of  a  Streamer  from 
the  Sun,  which  will  just 
be    Visible    at    the    ©'s 
Pole=/-V 

-4-15° 

+  7°.25 

1.64 

+15 

+  7.25 

6.42 

+15 

0. 

2.86 

+30 

0. 

1.00 

+30 

+  7.25 

0.65 

+30 

+  7.25 

1.59 

A  simple  way  to  represent  graphically  the  apparent  changes 
in  the  form  and  position  of  a  streamer,  due  to  the  change  in 
the  position  of  the  Earth  and  to  the  rotation  of  the  Sun,  is  to 
construct  a  model  of  a  single  streamer  issuing  from  a  sphere 
and  to  project  the  streamer  on  a  plane  surface  by  parallel  rays 
of  light.  If  the  sphere  be  rotated,  and  the  inclination  of  the 
axis  of  rotation  varied  between  the  proper  limits  (correspond- 
ing to  the  positions  of  the  Earth  at  different  seasons  of  the 
year),  all  the  peculiarities  of  the  appearances  of  the  coronal 
streamer  can  be  reproduced  and  studied  at  leisure. 

In  order  to  show  more  forcibly  the  varying  form  and  position 


10        A  Mechanical  Theory  of  the  Solar  Corona, 

of  a  streamer  in  projection,  I  have  exaggerated  the  curvature  in 
the  model  used  for  obtaining  the  outline  given  in  Plate  VIII. 

The  streamer  represented  by  a  wire  rod  was  made  to  issue 
from  a  latitude  of  about  15°,  and  to  have  such  a  length  that  in 
projection  it  was  just  visible  at  the  pole  for  j3  =  0°.  A  longer 
streamer  would  have  necessitated  the  use  of  a  smaller  scale. 

The  figures  at  the  extremities  of  the  lines  representing  the 
streamers  correspond  to  the  number  of  days  elapsed  since  the 
base  of  the  streamer  was  on  the  central  meridian  of  the  nearer 
hemisphere. 

Fig.  1,  of  Plate  VIII.,  corresponds  to  an  inclination  ft  =  0, 
Fig.  2  to  the  time  when  the  Earth  is  near  its  maximum  dis- 
tance below  the  plane  of  the  Sun's  equator,  and  Fig.  3  to  the 
time  when  the  Earth  is  near  its  maximum  distance  above  the 
same  plane. 

The  general  outlines  of  the  figures  on  Plate  VIII.  are  evidently 
the  same  as  would  be  produced  by  a  series  of  equidistant 
streamers  issuing  from  a  single  latitude  only. 

If  now  the  streamers  issue  from  different  latitudes  within 
the  limits  of  the  Sun-spot  zones,  coronal  forms  similar  to  those 
shown  on  Plate  VI.  (which  are  made  from  an  actual  model,  as 
described  on  the  plate  itself )  will  be  produced.  In  a  typical 
corona  the  mean  latitude  of  the  zone  from  which  the  streamers  issue 
will  always  be  the  same  as  the  latitude  of  the  densest  and  most 
extended  portion  of  the  coronal  outlines.  A  necessary  consequence 
of  the  perspective  overlapping  of  these  streamers  is  the  production 
of  luminous  rays  which,  in  a  typical  corona,  incline  away  from  the 
adjacent  poles,  as  will  be  demonstrated  further  on. 

A  crucial  test  of  this  or  any  other  theory  of  the  corona  is 
afforded  by  the  appearance  and  behavior  of  these  so  called 
"polar  rays"  If  they  really  originate  at  or  very  near  the  Sun's 
polar  regions,  the  laws  governing  their  appearance  must  be 
sought  for  in  the  physics  of  the  Sun  itself.  If,  however,  the 
present  conception  of  their  origin  is  the  true  one,  they  are 
mainly  due  to  a  series  of  apparent  intersections  of  streamers 
from  the  Sun's  equatorial  region,  projected  by  perspective  above 
or  below  the  poles;  that  is,  the  polar  rays  which  we  see  in  any 
corona  have  no  objective  existence.  The  situation  and  curva- 
ture of  these  rays  and  the  apparently  vacant  spaces  where  such 
rays  seem  to  be  wanting  (the  so  called  "rifts")  can  be  accu- 


PLATE  VIII. 


DIAGRAM  ILLUSTRATING  VARIATION  IN  THE  CURVATURE  AND  POSITION 
OF  A  SINGLE  STREAMER  IN  PROJECTION,  BY  J.  M.  SCHAEBERLE. 


By  J.  M.  Schaeberle.  11 

rately  observed,  and  the  present  theory  enables  one  to  account 
for  such  rays  and  rifts,  and  to  give  the  inclinations  and  general 
directions  of  their  curvatures. 

We  will  now  proceed  to  investigate  the  curvatures  and  situa- 
tions of  the  polar  rays,  first  deducing  the  expressions  which 
give,  in  projection,  the  positions  and  curvatures  of  the  streamers. 

I  call  a  "streamer"  the  actual  stream  of  particles  ejected 
from  the  Sun.  I  call  a  "ray"  the  subjective  appearance  pro- 
duced by  overlapping  streamers  seen  in  projection,  and  I  write 
"ray"  in  italics. 

We  will  first  consider  the  problem  for  the  case  when  fi=Q. 
Let  T  denote  the  heliocentric  longitude  of  the  base  of  a  streamer 
in  latitude  cp,  and  let  the  longitude  of  the  Earth  be  r0,  the  plane 
of  the  Sun's  equator  being  taken  as  the  fundamental  plane.  A 
normal  in  latitude  cp  and  longitude  t  —  r0  will  in  projection  inter- 
sect the  Sun's  limb  at  a  polar  distance  p  given  by  the  equation: 

(12) 


tan  cp 

The  position  angle  pf  of  the  inclined  stream  for  moderate  polar 
distances  can  then  be  found  from  the  approximate  expression: 

cos  (*—  TQ)  (13) 


The  inclination  (  J")  of  the  stream  to  a  normal  through  its 

base  will  in  projection  be  given  by  the  approximate  expression: 

jr,_/cos(r—r0) 


Finally,  the  inclination  T  to  a  normal  passing  through  the 
point  at  which  the  inclination  is  required,  will  be  approxi- 
mately: 

r=r-(p-p')  (15) 

Now,  owing  to  the  inclinations  of  the  streamers,  it  is  at  once 
evident  that  even  when  they  are  uniformly  distributed  in  longi- 
tude, they  can  never  be  symmetrically  arranged  around  a  radius- 
vector  of  the  Earth.  In  projection,  however,  an  approach  to 
a  symmetrical  form  results  from  a  peculiar  but  well  known 
optical  phenomenon. 

The  streamers  which  have  the  least  inclination  to  the  line  of 
sight  will  evidently  appear  to  be  most  widely  separated;  that 
is,  they  will  always  be  at  the  areas  of  minimum  density.  For 
the  nearer  hemisphere  the  minimum  density  in  projection  will 


12        A  Mechanical  Theory  of  the  Solar  Corona, 

evidently  always  be  just  a  little  to  the  west  of  the  Sun's  pole, 
while  for  the  farther  hemisphere  it  will  be  to  the  east  of  the 
Sun's  pole. 

Again,  as  the  streamers  are  slightly  curved,  those  having  the 
least  inclination  to  the  line  of  sight  will  in  projection  appar- 
ently have  the  greatest  inclination  with  reference  to  normals. 
Hence,  when  the  Earth  is  near  either  node,  an  approximately 
uniform  distribution  in  longitude  of  streamers  from  a  given 
latitude  cp  will  result  in  the  following  arrangement  in  ortho- 
graphic projection: 

As  streamers  issuing  from  the  nearer  hemisphere  have  an 
eastward  inclination  with  reference  to  normals,  the  two  areas 
of  minimum  density  will  be  a  little  to  the  west  of  the  Sun's 
poles;  while  for  the  farther  hemisphere  as  the  streamers  have 
a  westward  inclination  with  reference  to  normals,  the  corre- 
sponding areas  of  minimum  density  will  be  a  little  to  the  east 
of  the  Sun's  poles. 

The  inclination  to  the  normal  is  greatest  near  the  points  of 
minimum  density,  and  this  inclination  gradually  grows  less 
and  the  density  greater  as  the  angular  distance  from  these 
points  increases,  until  the  polar  distance  90° — cp  is  reached, 
where  the  inclination  to  the  normal  is  practically  zero,  and  the 
density  at  a  maximum.  ( See  illustrations  of  model,  Plate  VIII. ) 

The  apparent  intersections  of  these  streamers  produce  false 
streamers,  which  I  have  called  rays,  to  distinguish  them  from 
the  streamers  proper. 

The  form  of  these  rays  for  a  theoretical  corona  can  be  deter- 
mined after  the  method  which  will  now  be  considered. 

THEORY  OF  THE  INCLINED  RAYS. 

From  a  series  of  experiments  I  have  derived  the  expressions 
given  below,  which  govern  the  formation  of  certain  luminous 
lines  (which  for  want  of  a  specific  name  I  shall  simply  call 
rays)  produced,  as  is  well  known,  by  the  overlapping  of  two 
or  more  sets  of  alternate  bright  and  dark  lines. 

If  a  set  of  parallel  luminous  lines,  separated  by  the  small 
angular  distance  D,  is  crossed  at  the  small  angle  J  by  a  second  set 
of  parallel  lines  separated  by  the  slightly  less  angular  distance  D', 
then  when  either  set  is  viewed  through  the  other,  a  new  and  heavier 
set  of  luminous  lines  (rays)  will  be  formed,  which  make  the  angle 


By  J.  M.  Schaeberle.  13 

K  with  the  wider  set  of  lines,  and  the  angle  K  —  /  with  the  set  of 
closer  lines. 

I  have  deduced  the  following  rigorous  expression  for  the 
value  of  K: 

tan  g==         _?  -  r  tan  J  (16) 

D  —  DsecJ 

The  perpendicular  distance  Dl  between  two  adjacent  lines 
(rays)  of  the  new  set  is  given  by  the  rigorous  expression: 

D1=D(cot  /—cot  #)sin  K  (17) 

'Equation  (16)  shows  that  K  is  always  greater  than  J,  and 
reaches  a  maximum  when  D  —  D'sec  J=0;  for  this  condition 
#=90°,and  Dl=D  cot/. 

As  the  angle  /  increases,  the  number  of  intersections  to  a 
given  surface  increases.  Now  as  these  intersections  cause  the 
phenomenon  of  the  inclined  rays  (a  ray  passes  through  those 
intersections  which  are  nearest  together),  it  is  evident  that  the 
rays  will  be  least  conspicuous  when  the  number  is  greatest, 
since  the  contrast  between  different  parts  of  a  surface  covered 
by  such  rays  diminishes  as  the  intervals  grow  smaller. 

If  one  of  the  two  sets  of  lines  is  doubled  by  interpolating  a 
new  line  midway  between  each  of  two  adjacent  lines,  a  new  ray 
will  be  formed  midway  between  each  of  the  original  rays. 

Similarly,  if  both  sets  of  lines  be  supposed  to  change  in  the 
same  way,  precisely  the  same  effect  will  be  produced,  the  num- 
ber of  rays  being  quadrupled. 

If  this  process  of  bisection  is  continued  indefinitely,  a  limit 
is  soon  reached  at  which  the  lines  and  rays  form  a  practically 
continuous  surface.  The  inclination  of  these  rays  always  remains 
parallel  to  the  original  direction  corresponding  to  the  particu- 
lar condition  D  —  D'=x]  the  K  for  this  particular  series  of  rays 
can  be  distinguished  from  other  series  of  less  conspicuous  rays, 
made  by  the  same  set  of  lines,  by  writing: 


The  values  of  K  for  each  of  the  other  sets  of  inconspicuous 
rays  can  be  found  by  substituting  in  (17'),  successively,  the 

jy   jy    jy  T\> 

values  _,_,--_    ._.--^-,  in  place  of  D'. 

The   most   favorable    case    for   conspicuous   rays   evidently 


14        A  Mechanical  Theory  of  the  Solar  Corona, 

results  when  /  is  small,  and  D—D'=x  (x  being  a  small  quan- 
tity), since  for  these  conditions  any  two  intersecting  lines 
have  many  points  in  common,  supposing  the  lines  to  have 
sensible  breadths,  and  only  one  value  of  K  is  possible,  so  that 
all  the  rays  are  inclined  in  the  same  direction,  thus  at  once 
rendering  them  unmistakable. 

Equation  (17)  shows  that  so  long  as  J  is  very  small,  the 
number  of  rays  increases  very  rapidly  as  J  increases.  For 
large  values  of  J,  therefore,  no  conspicuous  rays  will  be  shown. 

As  the  angle  J=2I'  will  always  be  small  so  far  as  the  pres- 
ent investigation  is  concerned,  we  can,  without  appreciable 
error,  write,  in  place  of  equation  (16),  the  expression: 

tan  K=-^-p  tan  /  (18) 

I  tried  to  deduce  a  rigorous  expression  for  the  equation  of 
the  curve  formed  by  the  projection  of  the  nearer  set  of  stream- 
ers upon  the  farther  set,  but  found  the  conditions  too  compli- 
cated, since  there  are  two  sets  of  curved  diverging  lines,  neither 
set  having  a  common  point  of  intersection,  and  the  two  sets 
having  different  envelopes,  while  the  angle  of  divergence  itself 
is  a  variable  quantity. 

We  can,  however,  apply  the  above  formula  for  finding  K,  if 
we  consider  only  very  short  portions  of  the  curve,  since  for 
very  short  distances  the  deviation  from  parallelism  of  two 
adjacent  streamers  will  be  small,  and  consequently  the  error  in 
K  will,  as  a  rule,  be  small  also. 

Now  for  a  series  of  normals,  radiating  at  regular  intervals 
from  a  small  circle  whose  latitude  is  cp,  the  angle  between  the 
normals  in  the  nearer  and  farther  hemispheres  for  the  same 
position-angle  p  is  always  zero  in  projection;  hence  K  is  always 
zero,  whatever  the  relative  density  of  the  normals  in  the  two 
hemispheres  may  be.  The  projected  intervals  will  not  vary  as  a 
function  of  p  alone,  since  for  normals  in  latitude  (p,  the  density 
will  be  at  a  maximum  when  p=$Q°  —  cp;  hence  it  follows  that 
the  intervals  vary  as  some  function  of  ap,  a  being  defined  by: 


Now,  in  the  case  of  an  actual  streamer,  when  the  base  is  in 
longitude  r  —  TO)  the  longitude  indicated  by  the  direction  of  the 


By  J.  M.  Schaeberle.  15 

stream  at  a  distance  p  from  the  base  will  be  (r  —  TO  —  /');  hence, 
when  the  direction  of  the  streams,  at  a  distance  p,  corresponds  to 
T  —  T0=0  and  T  —  TQ=180°,  the  bases  of  these  streams  will  be 
in  longitudes  -{-I'  and  180°-+-!',  respectively.  Now,  in  projection, 
the  position-angles,  p^  and  p2  corresponding  to  these  longitudes, 
are  given  by  the  approximate  expressions: 


sn 


In  which  1=  -$—((&  —  &0),  p  being  measured  from  the  north 
pole  towards  the  east,  through  360°. 

Pi  and  p2  will  be  called  the  secondary  coronal  poles  of  the 
nearer  and  farther  hemispheres,  respectively,  for  the  latitude  (p. 

The  location  of  the  secondary  poles  can  perhaps  be  better 
understood  from  what  follows. 

At  the  north  pole,  for  example,  streamers  from  the  nearer 
hemisphere,  which  are  projected  on  the  west  side  of  the  second- 
ary pole,  appear  to  radiate  from  points  which  are  below  the 
Sun's  center.  As  the  position  angle  increases,  the  center  of 
divergence  appears  to  approach  the  Sun's  center,  and  then  to 
rise  above  it,  so  that  streamers  on  the  east  side  appear  in  pro- 
jection to  radiate  from  points  above  the  Sun's  center. 

Consequently,  at  the  same  true  polar  distances,  the  density 
on  the  east  side  of  the  Sun  will  be  greater  than  it  is  on  the 
west  side.  For  the  streamers  of  the  farther  hemisphere  pro- 
jected at  the  same  pole,  the  arrangement  is  evidently  exactly 
the  reverse. 

A  streamer  is  at  a  secondary  pole  when  its  direction  in  projec- 
tion is  parallel  to  the  Sun's  axis. 

Equation  (16)  can  be  written: 

tan  K=  --  ^—  —  tan  /  (21) 


From  which  it  appears  that  K  is  only  dependent  on  the  ratio 
of  D'  to  D,  and  entirely  independent  of  their  absolute  values. 

Let  us  consider  /  to  be  positive  when  the  inclination  of  the 
denser  set  of  projected  streamers  to  the  less  dense  set  is  in  the 


16        A  Mechanical  Theory  of  the  Solar  Corona, 

direction  N.E.S.W.,  and  negative,  when  the  inclination  is  in 
the  opposite  direction;  then,  in  conformity  with  the  law  stated 

on  page  58,  the  factor: 

D 
D—D' 

will  be  positive  in  the  first  and  second  quadrants  (but  inde- 
terminate between  the  limits  _p=90° — cp  and  90°+^?),  and 
negative  in  the  third  and  fourth  quadrants  (but  indeterminate 
between  the  limits  p=27Q°—(p  and  270°+^);  hence,  ac- 
cording to  the  above  equation,  K  will  always  have  the  same 
sign  as  J",  or,  in  other  words,  the  rays  in  latitudes  greater  than 
<p  will  always  be  inclined  in  a  direction  away  from  the  nearer 
pole.  The  angle  which  the  ray  makes  with  a  normal  will  be 
K — fj,  but  as  /  is,  as  a  rule,  smaller  than  the  error  of  the 
measured  inclinations,  and  /  always  less  than  0.5,  the  term  f'J 
can  be  neglected.  K  can  therefore  be  considered  to  be  the 
inclination  of  the  ray  to  a  normal,  and  if  the  quadrant  is 
mentioned  no  attention  need  be  paid  to  the  sign  of  K,  as  the 
inclination  is  in  the  direction  away  from  the  nearer  pole. 

For  finite  values  the  condition  D—D'  will  only  be  fulfilled  at 
the  poles  where  the  density  is  near  a  minimum;  the  very  short 
concentric  arcs  formed  by  the  few  intersections  of  nearly  normal 
streamers  inclined  to  each  other  at  the  small  angle  /,  will  there- 
fore not  be  visible  as  a  rule.  The  nearly  normal  rays  at  the 
poles,  therefore,  nearly  coincide  with  the  streamers.  This  par- 
ticular phase  of  the  phenomenon  is  beautifully  illustrated  by 
means  of  the  models  given  in  Plate  VII.,  described  further  on. 
Figure  I.  illustrates  one  of  the  cases  which  correspond  to  the 
the  value  /?=0°,  so  that  in  orthographic  projection  D=D'  at 
the  poles;  for  this  exceptional  position  the  slightest  variations 
of  the  angle  J",  produced  either  by  elevating  one  set  of  lines  with 
respect  to  the  other,  or  by  a  rotary  motion  of  the  plates,  causes 
the  ray  to  swing  very  rapidly  through  a  large  angle,  producing 
forms  like  Figures  II.,  III.,  IV.,  XV.,  all  corresponding  to  small 
values  of  J.  (Figures  X.  and  XI.  represent  conditions  when  J 
is  comparatively  large  and  D=D'.)  Except  for  critical  cases, 
a  given  value  of  .fiTdoes  not  change  to  any  great  extent  for  small 
relative  variations  of  Z),  D',  /,  as  can  be  seen  from  an  inspec- 
tion of  the  figures.  At  the  same  position-angle  p  the  Value  of 
K  will  vary  but  slightly  when  p  is  comparatively  large,  and 


By  J.  M.  Schaeberle.  17 

although  the  apparent  changes  are  very  rapid  for  a  given  ray, 
yet  as  each  one  assumes  a  new  position  another  ray  is  formed 
which  nearly  occupies  the  successive  positions  of  the  preceding 
ray,  so  that  at  any  given  instant  the  apparent  change  in  the 
whole  system  of  rays  will  only  result  in  a  lateral  displacement 
of  the  axis  of  symmetry,  and  for  the  critical  cases  the  concen- 
tric rays  formed  are  usually  not  of  sufficient  magnitude  to  be 
seen,  as  has  been  explained  above.  When  both  sets  of  stream- 
ers are  visible,  the  pyramidal  form  of  the  denser  portions  of  the 
rays  projected  at  the  poles  can  be  regarded  as  resulting  directly 
from  the  overlapping  of  streamers  inclined  to  each  other. 

Now  the  streamers  at  the  nearer  secondary  pole  are  projected 
against  streamers  of  the  farther  hemisphere,  which  are  at  an 
angular  distance  of  21  (=J)  from  the  farther  secondary  pole; 
for  the  polar  distance  p  the  ratio  of  the  intervals  D  and  D'  is 
therefore  a  function  of  ap  and  /'.  This  function  must  be  so  deter- 
mined that  the  density  is  least,  but  not  zero,  when  p=Q  ±  I', 
and  a  maximum  finite  density  when  p=90°  —  (p,  or  ap=90°. 

Let  #  and  d'  denote  the  densities  of  the  two  sets  of  streamers 
for  a  given  polar  distance  p.  We  then  have  as  a  rough  approx- 
imation for  values  of  p  greater  than  J  : 

d=d  sin  Op-f  /:) 
d'=d  sin  (ap—  I,} 

The  value  of  d  being  determined  by  the  condition: 

(23) 

In  which  S0  is  the  density  at  the  true  pole. 

In  place  of  the  density  tf,  we  can,  for  moderate  polar  dis- 
tances, substitute  the  reciprocal  of  the  corresponding  interval 
D,  and  write: 


Hence: 


D        d'      sin   (ap—I,) 
Substituting  this  value  of  the  ratio  of  the  intervals  in  equa 
tion  (21),  and  reducing,  we  obtain,  finally: 


tan  K=  -         tan  2T  (26) 

2cos  (ap)  sin  / 


18        A  Mechanical  Theory  of  the  Solar  Corona, 

21'  being  substituted  in  place  of  /.     As  /'  is  small  we  can 
write  tan  2/'—  2  tan/';  hence, 


tan  K=    Bn,    af-lr  tan  /'  (27) 

cos  (ap)  sin  J, 

The  ratio  of  tan  J7  to  sin  /x  will  be  practically  constant  for 
moderate  values  of  p.  When  ap=SQ°,  equation  (27)  becomes 
indeterminate.  If  the  streamers  were  of  infinitesimal  breadth 
in  latitude,  they  would  coincide  with  the  rays  when  p=9Q°  —  q>. 
In  reality,  however,  the  extension  in  latitude  may  be  consider- 
able, and  the  effect  of  this  extension  is  to  make  a  practically 
continuous  surface  of  rays  before  the  polar  distance  is  as  great 
as  90°  —  (p.  Hence,  polar  rays  at  considerable  polar  distances 
will  usually  be  lost  in  the  general  illumination. 

From  the  preceding  discussion  it  follows  that  for  the  case  of 
ft=Q°  the  axis  of  the  typical  corona  will,  in  orthographic  pro- 
jection, coincide  with  the  Sun's  axis. 

CHANGES  IN  THE  FORM  OF  THE  TYPICAL  CORONA  RESULTING 
FROM  VARIATIONS  IN  THE  HELIOCENTRIC  LATITUDE  OF  THE 
EARTH.  . 

When  the  Earth  is  above  (/?+)  or  below  (/?  —  )  the  plane  of 
the  Sun's  equator,  the  quantities  D,  /)',  and  /  undergo  certain 
changes  for  the  same  value  of  p  in  projection. 

When  the  Earth  is  below  the  plane  of  the  equator,  the  nearer 
streamers  of  the  northern  hemisphere  will  appear  more  dense, 
with  a  slightly  less  inclination  to  the  normal  than  is  the  case 
when  /?=0,  while  the  density  of  the  streamers  from  the  farther 
hemisphere  will  be  diminished;  but  the  increase  in  the  west- 
ward inclination  to  the  normal  will  be  greater  than  the  dimi- 
nution of  the  eastward  inclination  in  the  nearer  hemisphere. 
j  has  therefore  increased,  but  this  increase  is,  in  part,  at  least, 

counteracted  by  the  decrease  in  the  value  of  the  factor  —  —  —  ,. 

D  —  D  ' 

With  reference  to  the  streamers,  therefore,  K  does  not  neces- 
sarily change  to  any  great  extent.  But  as  the  nearer  streamers 
have  a  less  eastward  inclination,  while  the  farther  ones  have  a 
greater  westward  inclination,  the  whole  system  of  rays  formed 
will,  according  to  the  fundamental  principle  laid  down  in  the  law 
given  on  page  58,  have  a  greater  eastward  inclination.  The 


By  J.  M.  Schaeberle.  19 

effect  of  this  comm.on  change  in  the  inclination  of  the  rays  is  to 
cause  an  apparent  shifting  of  the  coronal  pole  towards  the  WEST. 

For  the  same  reason  the  south  coronal  pole  will  be  shifted 
towards  the  EAST. 

When  the  Earth  is  above  the  plane  of  the  equator,  the  north 
pole  of  the  corona  will  be  on  the  east  side  of  the  projected  posi- 
tion of  the  Sun's  pole,  and  the  south  coronal  pole  will  lie  on 
the  west  side. 

As  the  projections  seen  from  the  Earth  are  not  strictly  ortho- 
graphic, the  parallactic  effect  has  a  constant  tendency  to  throw 
both  coronal  poles  slightly  towards  the  east  of  the  position  they 
would  occupy  if  viewed  from  an  infinite  distance. 

Changes  in  the  form  of  the  typical  outer  corona,  due  to  varia- 
tions in  ft,  for  streamers  of  a  given  magnitude  and  distribution, 
can  be  readily  understood,  with  the  aid  of  the  prints  and  dia- 
grams given  in  Plates  VI.  and  VIII.,  in  connection  with  Tables 
IV.  and  V.,  and  also  from  what  follows  further  on. 

A  want  of  uniformity  in  the  distribution  of  the  streamers  in 
longitudes  r — rQ  =  ±0,  or  180°,  may  result  in  the  partial  or 
total  destruction  of  the  symmetrical  inclined  polar  rays,  and  in 
other  longitudes  the  same  irregularities  will  cause  a  deforma- 
tion of  the  general  typical  features  of  the  corona.  An  unsym- 
metrical  corona  is,  therefore,  in  no  way  to  be  regarded  as 
contrary  to  the  theory. 

If,  for  any  cause,  there  is  real  or  apparent  periodic  variation 
in  the  mean  latitude  of  the  streamers,  the  ratio  of  the  polar  to 
the  equatorial  extension  will,  of  course,  be  subject  to  a  similar 
variation.  (See  postscript.) 

From  Table  IV.,  we  see  that  for  two  streamers  in  latitude  15° 
and  30°,  respectively,  just  visible  at  the  poles  in  projection,  the 
one  in  latitude  30°  will  have  only  about  one  third  of  the 
equatorial  extension  that  is  shown  by  streamers  in  15°  latitude. 
If,  therefore,  the  mean  latitude  of  greatest  solar  activity  is 
apparently  shifted  towards  the  higher  regions  of  the  Sun-spot 
zones,  the  coronal  outlines  may  become  practically  circular. 
The  criterion  for  determining  from  the  observed  outlines 
whether  ft  is  large  or  small  will  no  longer  be  satisfactory,  since 
the  ratio  of  the  polar  to  the  equatorial  extension  now  under- 
goes but  a  slight  change  for  all  possible  values  of  ft.  However, 
when  the  polar  rays,  or  the  wing  boundaries  adjacent  to  the  poles, 
3s 


20        A  Mechanical  Theory  of  the  Solar  Corona, 


are  present,  the  position  of  the  axis  of  the  inner  corona  will,  as 
a  rule,  at  once  tell  whether  the  observer  was  above,  below,  or 
in  the  plane  of  the  Sun's  equator.  The  inclinations  of  the 
boundaries  of  the  wings,  at  the  Sun's  outline,  can  be  used  to 
indicate,  approximately,  the  position  of  the  pole  of  the  inner 
corona  when  the  rays  are  wanting. 

Now,  when  the  Earth  is  at  considerable  distances  above  or 
below  the  pl'ane  of  the  Sun's  equator,  and  the  equatorial  stream- 
ers are  visible  for  only  a  moderate  distance,  the  more  depressed 
set  may  show  so  faintly  that  they  apparently  fall  short  of  reach- 
ing the  pole  in  projection.  For  this  case,  equation  (16)  shows 
that  K=0,  since  21'  is  then  zero;  so  that  if  all  the  streamers 
were  confined  to  a  single  circle  of  latitude  and  only  one  set  vis- 
ible at  the  pole,  the  true  projections  of  the  streamers  would  be 
seen,  and  the  direction  of  curvature  would  always  be  governed 
by  rigorous  conditions.  (See  Plate  VIII.) 

For  this  case,  when  the  symmetrical  inclined  rays  are  present, 
the  phenomenon  admits  of  the  same  simple  explanation,  which 
accounts  for  the  polar  rays  when  fi  is  nearly  zero,  since  stream- 
ers on  opposite  sides  of  the  Sun,  whose  latitudes  differ  by  2ft, 
will,  in  projection  at  the  poles,  produce  a  similar  arrangement 
of  the  rays;  but  these  rays  will  not  necessarily  extend  to  the 
outer  limit  of  the  coronal  structure  at  the  poles,  and  for  this 
reason  they  may  not  be  conspicuous  when  ft  is  large. 

When,  however,  the  polar  rays  are  very  conspicuous  and 
uniform  for  large  values  of  /3,  and  a  small  equatorial  extension, 
the  phenomenon  is  still  to  be  accounted  for  in  the  same  general 
way,  which  we  will  now  consider. 

As  the  curvature  and  deviation  from  the  normal  depend  in 
projection  upon  the  latitude  q>,  streamers  in  different  latitudes 
with  nearly  the  same  longitude  will,  in  projection,  apparently 
intersect  each  other,  and  consequently  curved  rays  or  outlines 
will  be  formed,  and  these  may  be  wholly  produced  in  either  the 
nearer  or  farther  set  of  streamers.  For  the  same  position-angle 
p,  streamers  in  latitude  cp'  will  not  appear  to  radiate  from  the 
same  points  that  those  in  latitude  cp  do.  If  the  secondary  poles 
for  latitude  cp'  are  given  by  the  expressions: 

p i '  =  —  /! '  nearer  hemisphere,  fr><-.. 

p2'  =  +  //  farther  hemisphere, 

Then  for  -f  cp'  greater  than  -f-  cp  we  would  always  have  //  less 
than  /!.  This  results  directly  from  the  fact  that  the  change  in 


By  J.  M.  Schaeberle.  21 


the  directions  of  the  streams  varies  nearly  with  p2,  and  in  pro- 
jection at  the  poles  the  ratio  of  p  to  p'  is  nearly  the  same  as  the 
ratio  of  cosec  cp  to  cosec  qj '.  The  streamers  in  latitude  (p  will 
therefore  be  more  inclined  to  the  normal  than  those  in  latitude 
(p'.  In  projection,  therefore,  streamers  on  the  east  side  of  the 
secondary  pole  in  latitude  (p  will  appear  to  radiate  from  points 
which  are  nearer  than  the  corresponding  points  for  latitude  cp', 
while  on  the  west  side  of  the  Sun  the  points  on  the  osculating 
curves  are  at  greater  distances  for  latitude  cp  than  they  are  for 
the  latitude  cp' .  The  resulting  apparent  variation  in  density  will 
therefore  produce  the  same  phenomenon  which  results  from  the  pro- 
jection of  the  streamers  of  the  nearer  hemisphere  upon  those  of  the 
farther.  Inclined  polar  rays  may  therefore  be  formed  by  the  over- 
lapping of  streamers  having  nearly  the  same  longitude  but  differ- 
ent latitudes.  For  this  case  the  /j  of  equation  (24)  would  be 
the  angular  distance  between  the  secondary  poles  for  latitude 
cp  and  cp',  while  /'  would  correspond  to  the  difference  of  the  pro- 
jected inclinations  at  the  pole  for  the  given  latitudes. 

If  we  assume  the  ratio  of  the  latter  to  the  former  to  be  c, 
and  neglect  the  small  angle  (II — 7/),  equation  (27)  reduces  to: 

tan  K=c  tan  (ap')  (29) 

In  which  p'  is  now  the  distance  from  the  mean  secondary  pole. 
This  system  of  rays  will  be  more  probable  for  large  values  of 
/?,  and  will  not  be  symmetrical  with  reference  to  the  poles  of 
the  Sun.  The  inclinations  will  vary  with  the  value  of  c;  these 
variations  will,  however,  as  a  rule,  be  small,  since  the  values 
of  /?,  cp,  and  cp'  are  subject  to  comparatively  small  variations. 

When  ft  is  zero,  the  streams  of  the  nearer  hemisphere  pro- 
jected against  those  of  the  farther  hemisphere  will  produce  a 
corona  whose  axis  will  be  practically  coincident  or  parallel  with 
the  Sun's  axis.  The  density  (in  projection)  at  the  poles  may  at 
times  be  so  great  that  only  the  wings  are  seen;  the  boundary  of 
these  wings,  even  at  the  poles,  will  then  extend  to  a  limit  at 
which  the  polar  rays  begin. 

Equation  (21)  shows  that  the  inclination  of  the  rays  is  inde- 
pendent of  the  magnitude  of  the  intervals,  so  that  even  when 
the  density  is  very  great  or  very  small,  the  inclination  K  of  the 
polar  rays,  when  these  are  present,  will,  for  a  given  value  of  ft, 
always  be  practically  the  same  for  a  uniform  distribution  of  the 
streamers. 


22        A  Mechanical  Theory  of  the  Solar  Corona, 

The  four  great  curves  which  bound  the  outer  portions  of  the 
wing-like  coronal  outlines,  which  form  a  prominent  feature  of  so 
many  eclipses,  are  the  envelopes  of  the  outer  portions  of  the 
streamers,  the  density  at  points  on  the  envelopes  being  such 
that  the  intervals  are  just  filled  out.  The  positions  of  these 
envelopes  are  largely  determined  by  the  projection  of  the  more 
depressed  set  of  streamers  against  the  more  elevated  set,  or 
vice  versa.  (See  Plate  VI.) 

To  obtain  an  approximate  analytical  expression  for  these 
envelopes,  let  y-f  be  the  distance  from  the  Sun's  center  to  the 
point  on  the  Sun's  axis,  where  one  set  of  streamers  in  latitude 
q>,  produced  backward,  would,  in  projection,  just  form  a  con- 
tinuous surface,  and  let  Pf  be  the  polar  distance  of  the  point 
where  the  boundary  of  this  continuous  surface  cuts  the  limb  of 
the  Sun  in  projection.  Then  the  distance  y',  at  which  the  inter- 
vals between  adjacent  streamers  will  just  be  filled  out  for  differ- 
ent values  of  p,  will  be  approximately  given  by  the  expression: 

Y  —  7i  sec  (ap)  (30) 

In  which  yf  is  a  function  of  the  actual  density,  and  equal  to 
the  distance  from  the  Sun's  center  to  the  point  where  the 
envelope  proper,  or  the  envelope  produced,  cuts  the  Sun's  axis. 

For  values  of  y',  less  than  the  Sun's  radius,  the  approxi- 
mate expression  (31)  will  answer: 

7/1  ="  sec  (a**)  (31) 

For  the  envelope  of  the  other  set  of  streamers,  projected  at 
the  same  pole,  we  have: 

y"=y"  sec  (ap)  (32) 


Similarly,  streamers  in  latitude  ?/,  cp",  etc.,  will  have  envel- 
opes of  the  same  general  character.  The  overlapping  of  all 
these  envelopes  finally  produces  the  outlines  of  the  four  great 
wings. 

The  principal  boundary  curve  or  curves  will  be  approx- 
imately represented  by  the  equation: 

r=ylSec(ap)  (34) 

The  value  of  yl  being  found  from  data  taken  directly  from 
the  photographs. 


By  J.  M.  Schaeberle.  23 


Equation  (34)  is  the  locus  of  a  curve  of  indefinite  extent, 
which  leaves  the  Sun's  surface  at  the  polar  distance  P,  or  cuts  the 
Sun's  axis  at  a  distance  y±  from  the  Sun's  center,  the  inclination 
to.  the  normal  varying  from  90°  for  p=Q  to  0°  for  p=90° — q>. 
The  curve  has  for  its  asymptote  a  produced  diameter  of  the 
Sun  in  a  position-angle  nearly  equal  to  90° — cp  ,  in  which  q)m 
is  the  mean  latitude  of  the  streamers. 

If  the  distribution  of  the  streamers  in  longitude  is  not  uni- 
form, equation  (34)  will  not  necessarily  represent  the  observed 
form  for  small  values  of  p,  and  if  the  terrestrial  atmospheric 
conditions  are  unfavorable  for  showing  the  outer  corona,  the 
same  equation  will  apparently  fail  when  p  is  large. 

The  inner  boundaries  of  these  wings  will  be  determined  by 
similar  conditions.  As  the  forces  at  the  equator  are  presum- 
ably less  active  than  those  having  a  small  latitude,  the  envel- 
ope of  these  portions  of  the  projected  streams  will  in  general  be 
concave  near  the  Sun's  disk.  The  closing  of  the  wings  (or 
fish  tails  as  they  are  sometimes  called)  and  the  decrease  in 
density  of  the  exterior  boundaries,  result  directly  from  a  grad- 
ual increase  in  the  value  of  ft. 

The  trumpet-shaped  outline  of  the  more  distant  portions  of 
the  wings  which  were  first  photographed  in  January,  1889,  is 
theoretically  just  what  is  called  for.  Since  the  brightness  of 
the  streamers  decreases  with  increasing  distances  from  the 
Sun's  surface,  the  illumination  can,  by  contrast,  only  be  of 
indefinite  extent  in  those  directions  where  many  of  these  stream- 
ers overlap  each  other,  that  is,  in  position-angles  corresponding 
to  ±(90°— -<p)  and  ±(270°— <p).  The  equation  of  the  outer 
boundary  curve  is  nearly  of  the  form  expressed  by  formula 
(34). 

The  figures  given  in  Plate  VI.  would  be  still  more  strikingly 
similar  to  coronal  outlines  were  it  practicable  to  represent  the 
decrease  in  the  brightness  of  the  streamers  (represented  by  the 
needles  in  the  model)  with  increasing  distances  from  the  center. 

POLAR  GAPS  OR  RIFTS. 

There  are  several  different  causes  which  unite  to  produce  an 
apparent  extinction  of  the  polar  rays  for  increasing  polar  dis- 
tances. The  first  of  these  is  made  evident  from  the  following 
considerations:  Viewed  from  a  given  point,  a  series  of  equally 


24       A  Mechanical  Theory  of  the  Solar  Corona, 


bright  radial  lines  (and  practically  equidistant  from  the  ob- 
server) of  indefinite  extent  will  not  appear  equally  bright  to  the 
eye.  The  lines  which  are  less  inclined  to  the  visual  rays  will 
always  be  brighter  than  the  more  inclined  ones,  since  in  a  given 
direction  the  density  of  the  luminous  particles  which  make  up 
the  line  increases  for  decreasing  inclinations.  Hence,  at  a  given 
actual  distance  from  the  Sun,  a  streamer  will  appear  brightest 
when  it  is  projected  at  the  poles. 

A  second  reason  why  the  rays  at  the  pole  are  the  brightest  is 
the  following:  Beams  from  two  sources  of  light  of  the  same  abso- 
lute quantity,  but  of  different  angular  magnitude,  will  be  affected 
differently  in  passing  through  an  absorbing  medium  like  our 
atmosphere.  If  in  one  case  the  light  is  concentrated  in  a  series 
of  points  or  lines  in  a  given  surface,  and  in  the  other  case  the 
same  amount  of  light  is  distributed  over  the  whole  of  the  same 
surface,  the  absorbing  effect  of  our  atmosphere,  through  which 
the  two  sets  of  luminous  beams  pass,  will  be  more  marked  in  the 
latter  case  than  it  will  in  the  former.  Referring  now  to  the 
illustrations  given  in  Plate  VII.,  it  will  be  noticed  that  the 
number  of  rays  increases  with  the  inclination,  while  the  mag- 
nitude of  these  same  rays  decreases  with  the  inclination.  (In 
order  that  the  outer  extremity  of  an  inclined  ray  shall  be  at  as 
great  a  distance  from  the  Sun's  limb  as  a  ray  at  the  pole,  the 
ratio  of  the  length  of  the  former  to  the  length  of  the  latter 
must  be  nearly  as  sec  K  to  unity;  or,  for  the  same  length  of 
inclined  and  polar  rays,  the  corresponding  ratio  of  distances 
from  the  Sun's  limb  would  be  nearly  as  cos  K  to  unity.)  The 
absorbing  effect  of  our  atmosphere  will  therefore  always  have 
the  tendency  to  cause  a  greater  weakening  of  the  more  inclined 
rays  up  to  the  position  where  the  increase  in  density  suddenly 
rises  in  projection  (in  the  model  this  absorptive  effect  is  of 
course  not  included,  hence  the  gaps  are  not  strongly  shown), 
the  effect  of  which  is  to  cause  a  great  contrast  between  the 
comparatively  bright  boundaries  of  the  wings  and  the  more 
conspicuous  polar  rays.  An  inspection  of  the  best  photographs, 
however,  will  show  that  these  spaces,  apparently  devoid  of 
dense  coronal  matter,  are  often  really  filled  out  with  faint  rays, 
which  in  a  poor  photograph  would  not  show  at  all.  The  exist- 
ence of  rifts  in  other  positions  is  illustrated  in  the  models. 
When  the  density  of  the  streamers  is  so  small  that  no  definite 


By  J.  M.  Schaeberle.  25 

boundary  of  a  wing  is  formed,  the  rays  may  be  visible  to  a  polar 
distance  nearly  equal  to  90° — q>.  Even  if  the  streamers  are  not 
of  a  gaseous  character,  their  boundaries  will  not  be  sharply  de- 
fined, since  the  variation  in  latitude  results  in  intersections  at 
very  small  angles;  any  attempt,  therefore,  to  follow  the  course  of 
any  particular  one  of  these  streamers,  projected  as  it  is  against 
many  others,  may  be  wholly  in  vain. 

GRAPHICAL  REPRESENTATION  OP  POLAR  RAYS. 

In  the  model  (Plate  VI.)  the  diameter  of  the  needles  com- 
pared with  the  diameter  of  the  ball  is  too  great  to  admit  of  the 
use  of  a  sufficient  number  to  produce  the  phenomenon  of  inclined 
rays  satisfactorily. 

I  have,  however,  been  able  to  fulfill  the  conditions  imposed 
by  a  modification  of  the  graphical  method.  In  projection,  the 
streamers  near  the  poles  will  appear  to  be  tangent  to  a  small 
circle  concentric  with  the  Sun,  instead  of  passing  through  the 
Sun's  center.  Accordingly,  instead  of  using  slightly  inclined 
needles  radiating  from  the  surface  of  a  sphere,  I  formed  a  series 
of  alternate  bright  and  dark  lines  on  an  opaque  film  on  the 
surface  of  a  piece  of  plate  glass.  These  radial  lines  (slightly 
curved)  were  all  drawn  tangent  to  the  same  small  circle,  so  that 
for  a  given  distance  from  the  center  of  this  circle  the  inclination 
to  a  normal  was  approximately  the  same  as  required  by  theory. 
On  this  plate  a  second  plate  copied  from  the  first  was  laid,  in 
both  the  direct  and  reversed  positions. 

Now  the  condition  which  must  be  fulfilled  is  this:  The  lines 
of  one  plate  must  all  be  inclined  in  the  same  direction  with 
reference  to  the  lines  of  the  other  plate,  and  this  arrangement 
must  still  produce  rays  which  incline  away  from  the  lines  rep- 
resenting the  secondary  poles,  if  the  theory  is  true.  While  I 
had  no  doubt,  from  theoretical  considerations,  as  to  what  the 
pictorial  result  of  the  combination  of  the  two  gratings  would 
be,  I  had  hardly  hoped  to  obtain  such  satisfactory  results  on  a 
first  trial.  In  Plate  VII.,  Figures  I.,  II.,  III.,  IV.,  VIII.,  X.,  XL, 
XV.,  a  and  c  illustrate  some  of  the  many, forms  which  can  be 
produced  by  streamers  having  nearly  the  same  longitude,  but 
different  latitudes,  the  plates  for  this  purpose  being  superposed 
without  reversing.  The  remaining  prints  V.,  VI.,  VII.,  IX., 


26        A  Mechanical  Theory  of  the  Solar  Corona, 

XL,  XII.,  XIII.,  6,  d,  and  e,  illustrate  some  of  the  forms  pro- 
duced when  the  streamers  of  the  nearer  hemisphere  are  projected 
against  those  of  the  farther  hemisphere,  the  plates  being  reversed 
for  this  purpose.  The  shifting  of  the  secondary  coronal  pole  is 
also  represented  (see  Figures  VIII.  and  IX.,  Plate  VII.) ;  one  set 
of  lines  being  slightly  raised  or  lowered  to  correspond  to  a  change 
in  the  position  of  the  Sun's  axis,  which,  in  projection,  is  sup- 
posed to  be  parallel  to  the  edge  of  the  paper. 

The  original  prints  were  made  on  platinum  paper,  the  two 
superposed  gratings  representing  the  negative.  These  prints, 
like  those  of  Plate  VI. ,  were  then  fastened  to  a  large  sheet  and 
photographed  so  as  to  obtain  on  a  single  page  all  the  different 
forms  shown  in  Plate  VII. 

If  a  set  of  alternate  bright  and  dark  straight  lines  radiating 
from  the  same  point  is  placed  upon  another  set  of  lines  also 
radiating  from  a  point,  no  curves  will  be  formed  so  long  as  the 
centers  of  divergence  are  in  the  same  line  of  sight;  but  the 
instant  one  center  is  shifted  with  reference  to  the  other,  curves 
quite  similar  to  those  given  in  Plate  VII.  will  be  produced. 
If  the  plates  are  separated  from  each  other,  the  errors  in  the 
directions  and  positions  of  the  lines  will  have  a  much  less  dis- 
torting effect  upon  the  rays  than  when  the  plates  are  close 
together. 

For  the  purpose  of  making  the  prints,  however,  it  was  nec- 
essary to  place  the  plates  close  to  the  platinum  paper;  all  the 
irregularities  are  therefore  shown  in  these  prints.  It  must  be 
remembered  that  from  the  nature  of  the  model  the  outer  por- 
tions of  the  rays  shown  in  the  figures  of  Plate  VII.  are  much 
too  bright  and  prominent,  since  the  intensity  does  not  diminish 
with  the  distance  from  the  center  of  divergence,  as  it  evidently 
does  for  the  actual  corona. 

Then,  again,  in  the  model  the  contrast  between  the  bright 
and  dark  lines  is  abrupt  and  sharp,  so  that  in  the  prints,  for  a 
near  view,  these  lines  show  plainly  with  the  rays]  but  in  the 
case  of  actual  streamers  this  state  of  things  would  evidently 
not  exist.  If  the  plate  is  removed  several  feet  from  the  eye, 
only  the  rays  will  be  distinguishable  to  the  unaided  vision. 

NOTE.— If  each  eruption  is  regarded  as  resulting  in  a  large  number  of  slightly 
diverging  pencils  of  matter,  two  eruptions  on  the  central  meridian  in  slightly 
different  latitudes  would,  in  projection  at  the  poles,  also  cause  the  phenome- 
non of  inclined  rays. 


By  /.  M.  Schaeberle.  27 


If  several  plates  are  superposed,  the  contrasts  are  strength- 
ened, and  grotesque  figures,  resulting  from  irregularities  in  the 
gratings,  are  not  uncommon.  r,g 

The  boundaries  of  the  wings  in  tne  hemisphere  which  con- 
tains the  visible  pole  will,  even  for  comparatively  small  values 
of  /?,  usually  appear  double  or  multiple  on  the  side  turned 
toward  the  adjacent  pole,  as  portions  of  both  sets  of  streamers 
can  be  seen  directly. 

When  fi  is  exactly  zero,  and  the  density  of  the  streamers 
uniform  and  great,  the  outer  boundary  of  the  wings,  even  at  the 
poles,  may  inclose  the  area  usually  occupied  by  the  polar  rays. 
The  density  of  the  coronal  areas  will  then  increase  toward  those 
axes  whose  latitudes  are  the  same  as  the  mean  latitudes  of  the 
streamers.  The  outlines  of  the  fainter  and  more  distant  por- 
tions, rendered  visible  by  the  overlapping  of  many  faint  streamers 
projected  along  these  axes,  will  then  be  approximately  repre- 
sented by  equation  (34).  If,  however,  for  any  cause  the  stream- 
ers from  the  low  latitudes  are  not  decidedly  more  conspicuous 
than  those  in  higher  latitudes,  or  if  there  is  a  real  or  an  apparent 
periodic  increase  in  the  latitudes  of  the  streams,  which  at  times 
transfers  the  scene  of  greatest  visible  activity  to  the  higher  limits 
of  the  spot-zones,  the  outline  of  the  bounding  curves  of  the  wings 
is  more  likely  to  form  a  closed  figure,  and  the  general  coronal 
boundary  will  be  more  nearly  circular,  since  the  contrast 
between  the  areas  of  different  brightness  for  increasing  dis- 
tances may  not  be  sufficient  to  bring  out  the  envelope  whose 
approximate  equation  has  already  been  considered. 

From  what  has  already  been  said,  it  is  evident  that  the  con- 
dition of  the  Earth's  atmosphere  at  the  place  and  time  of  obser- 
vation, determines,  in  a  very  great  degree,  the  form  of  the  visible 
boundary  of  the  outer  corona. 

Before  giving  further  results  of  the  comparison  between 
theory  and  observation,  it  is  proper  to  make  a  few  remarks 
relating  to  the  difficulty  under  which  one  labors  in  making  an 
unbiased  examination  of  published  data  which  are  believed  to 
be  representations  of  a  certain  theoretical  form. 

One  is  very  apt  to  overestimate  the  importance  of  certain 
coincidences  and  to  disregard  as  unimportant  certain  discrep- 
ancies. For  instance,  some  of  the  evidence  tending  to  prove 
that  the  streamers  issue  from  the  Sun's  equatorial  regions 


28        A  Mechanical  Theory  of  the  Solar  Corona, 

depends  to  a  certain  extent  upon  the  observed  variations  of  the 
general  outlines  of  the  outer  corona  for  different  values  of  ft. 
So  far  as  this  particular  evidence  is  concerned  the  conclusion 
reached  must  depend  largely  upon  the  data  derived  from  mere 
drawings,  as  the  number  of  reliable  photographs  secured,  for 
different  eclipses,  is  hardly  sufficient  to  decide  the  case  def- 
initely. The  interpretation  of  these  drawings  and  poorer  pho- 
tographs, by  different  unbiased  observers,  will  not  necessarily 
be  the  same. 

Certain  features  should,  however,  always  be  present  in  good 
photographs,  giving  evidence  tending  to  prove  that  the  stream- 
ers originate  in  the  spot-zones;  of  these  the  equatorial  outlines 
of  the  outer  corona  are  perhaps  the  most  important.  The  vari- 
ation in  the  position  of  the  secondary  coronal  poles,  according 
to  the  position  of  the  observer  with  reference  to  the  Sun's  equa- 
tor, also  gives  decisive  evidence  on  this  point. 

For  those  eclipses  of  which  we  have  photographs  showing 
polar  rays  suitable  for  measurement,  I  have  used  the  constants 
for  a  mean  latitude  of  15°  for  the  streamers,  and  placed  /?— 0 
for  finding^.  As  the  exact  nature  of  the  distribution  of  the 
streamers  in  latitude  is  not  known,  any  attempt  to  take  into 
consideration  the  slight  variations  in  K,  due  to  variations  of  ft 
between  0°  and  8°,  in  order  to  obtain  a  closer  agreement  between 
theory  and  observation,  would  seem  to  be  superfluous.  For 
those  photographs  of  eclipses  in  which  the  rays  are  not  shown, 
I  have  used  the  following  method  for  obtaining  the  direction 
of  inclination  of  the  axis  of  the  inner  corona  with  reference  to 
the  Sun's  axis.  At  the  origin  of  the  curves  bounding  the  wings 
adjacent  to  the  poles,  tangent  lines  were  drawn.  Through  the 
two  points  of  intersection,  formed  by  the  two  lines  near  each 
pole,  the  coronal  axis  is  supposed  to  pass;  when  this  line  does 
not  pass  through  the  Sun's  center,  I  have  assumed  it  to  be  par- 
allel to  the  coronal  axis,  as  the  parallactic  effect  in  a  typical 
form  is  such  that  both  poles  of  the  corona  are  shifted  towards 
the  east  of  the  points  they  would  occupy  in  orthographic  pro- 
jection. The  data  for  finding  the  position  of  the  Sun's  center 
with  reference  to  the  center  of  the  Moon  is,  also,  nearly  always 
wanting. 

As  this  shifting  of  the  secondary  poles  will  ordinarily  be 
only  a  few  degrees,  I  have  preferred  to  refer  all  the  measures 


By  J.  M.  Schaeberle. 


29 


to  the  true  solar  poles,  rather  than  to  the  coronal  poles;  this 
treatment,  when  fl  is  large,  will  of  course  make  the  differences 
between  computation  and  observation  larger  than  they  would 
be  if  the  coronal  poles  were  taken  as  the  origin. 

For  the  above  named  conditions  we  therefore  have  for  the 
neighborhood  of  the  poles  and  at  the  Sun's  limb  the  following 
numerical  values: 
tan  lf 


Hence, 


-=c=1.5,  a=1.2,  and  Il=2 


tan  ^1-5  sin  d*  p- 

C08  (1.2  p) 


o. 


(36) 


The  following  are  the  numerical  values  of  K  for  each  10°  of 
distance  from  the  adjacent  pole: 


P 

10° 

20° 

30° 

40° 

K 

15° 

31° 

46° 

58° 

With  reference  to  the  form  of  the  outer  corona,  as  shown  by 
any  particular  photograph,  a  very  great  deal  depends  upon  the 
mode  of  development  of  the  photographic  plate.  A  corona  with 
great  equatorial  extension  can  be  made  to  appear  nearly  circu- 
lar, especially  if  the  atmospheric  conditions  at  the  time  of  an 
eclipse  are  poor,  so  that  only  the  brighter  parts  are  shown.  In 
dealing  with  drawings  not  made  from  photographs,  a  rude 
approximation  to  the  true  general  outline  can,  at  best,  only  be 
obtained  by  combining  the  results  of  many  different  observers 
of  the  same  eclipse.  Such  drawings  are  of  little  or  no  value 
for  determining  the  sign  of  ft.  The  individual  results  of  pure 
drawings  are  often  so  discordant  among  themselves  that  it  is 
difficult  to  comprehend  how  they  can  possibly  be  reconciled  so 
as  to  represent  the  same  phenomenon. 

Bearing  in  mind  the  fact  that  in  the  graphical  represen- 
tation the  intensity  or  distinctness  of  each  streamer  does  not 
decrease  as  the  distance  from  the  center  increases,  the  prints 
from  the  model,  of  which  illustrations  are  given  in  Plate  VI., 
can,  in  a  general  way,  be  used  to  represent  typical  coronas. 
The  outline  of  the  outer  corona  gives  a  rough  indication  of  the 
amount  of  the  inclination  of  the  Sun's  axis;  while  the  indi- 


30       A  Mechanical  Theory  of  the  Solar  Corona, 

cated  positions  of  the  poles  of  the  inner  corona  at  once 
determine  whether  the  observer  is  above  or  below  the  plane  of 
the  equator.  It  will  be  noticed  that  even  in  this  simple  model 
the  boundaries  of  the  wings  indicate  the  positions  of  the 
coronal  poles.  The  reason  why  the  polar  rays  are  not  satis- 
factorily formed  has  already  been  stated. 

TABLE  V.    (Plate  VI.) 


No.  of  Figure.  Corresponds  to  Season  of  the  Year. 


1-- 

End  of  November  and  beginning  of  December. 

I  

End  of  May  and  beginning  of  June. 

2,  3,  and  4  

End  of  December  and  beginning  of  January. 

5  

End  of  July  and  beginning  of  August. 

6  

End  of  January  and  beginning  of  February. 

7  

.  _    .                 End  of  February  and  oeginning  of  March. 

8  

.  -                  End  of  August  and  beginning  of  September 

OBSERVATIONS  OF  SOLAR  ECLIPSES  AND  COMPARISONS  WITH 
THEORY.* 

Eclipse  of  1715,  May  2. 

The  individual  drawings  and  descriptions  are  discordant 
among  themselves. 

1776,  February  9. 

Same  remarks  as  above. 

1806,  June  16. 

The  drawing  is  described  as  being  a  mere  diagram,  showing 
the  general  effect  of  the  light  about  the  dark  Moon.  Equatorial 
streamers  evidently  not  markedly  large.  (Maximum  of  spots, 
1804;  minimum,  1811.) 

1842,  July  8. 

Imperfect  records.  The  observers  supposed  the  equatorial 
extension  to  be  the  zodiacal  light.  Equatorial  extension  great. 
(Maximum  of  spots,  1837;  minimum,  1843.) 

*  All  the  references  are  to  A.  C.  RANYARD'S  work  "  Observations  made  during 
Solar  Eclipses,"  Mem.  R.  A.  S.,  Vol.  XLL,  unless  otherwise  stated.  To  make 
possible  a  comparison  between  the  variations  in  the  general  details  of  the 
corona,  as  influenced  by  the  phenomena  of  outgoing  streamers  retarded  by 
incoming  ones  (see  postscript),  I  have  added  the  times  of  maxima  and  minima 
of  Sun  spots,  as  determined  by  the  investigations  of  SCHWA  BE,  WOLF,  and 
others. 


By  J.  M.  Schaeberle.  31 


1851,  July  28. 

The  daguerreotype  taken  at  Konigsberg  shows  only  the  inner 
and  brighter  portions  of  the  corona.  The  resemblance  to  the 
inner  corona  of  July,  1878,  is  apparent.  As  required  by  the 
theory  for  a  typical  form,  when  ft  is  positive,  the  axis  of  the 
inner  corona  is  inclined  eastward,  according  to  the  inclination 
of  the  faint  boundaries  of  the  wings  just  visible.  (Maximum 
of  spots,  1848;  minimum,  1856.) 

1853,  November  80. 

RANYARD  gives  no  drawing  of  this  eclipse,  but  the  description 
is  just  what  the  theory  requires  it  to  be  when  the  Earth  is  near 
the  node.  (Five  years  after  maximum,  and  three  years  before 
minimum  of  spots.) 

1858,  September  7. 

The  drawing  in  general  agrees  with  the  form  required  by 
theory  'when  ft  is  large.  (Compare  with  Figure  7,  Plate  I.) 
(Minimum  of  spots,  1856;  maximum,  1860.) 

I860,  July  18. 

The  photograph  by  MONSERRAT  shows  only  the  innermost 
parts  of  the  corona.  The  faint  traces  of  the  wing  boundaries 
indicate  that  the  inner  coronal  axis  is  inclined  towards  the  east, 
as  it  should  be.  The  drawings  are  very  discordant  among  them- 
selves, and  show  much  polar  extension.  The  majority  of  the 
drawings  also  give  an  eastward  inclination  to  the  coronal  axis. 
Many  of  the  drawings,  especially  the  grotesque  one  by  TEMPEL, 
I  can  reproduce  almost  exactly,  with  a  model*  (Maximum  of 
spots,  1860.) 

1867,  August  18. 

No  photographs;  the  one  drawing,  which  does  not  agree  with 
the  description  by  the  observer,  shows  great  equatorial  exten- 
sion, with  only  a  few  short  rays  at  the  pole.  (Minimum  of 
spots,  1867.5.) 

1868,  August  18. 

All  the  drawings  agree  in  giving  evidence  of  a  considerable 
inclination  of  the  Sun's  axis.  (Compare  the  drawings  with  the 
denser  portions  of  Figure  5,  Plate  I.)  The  majority  of  the 
drawings  give  evidence  of  an  eastward  inclination  of  the  inner 


32        A  Mechanical  Theory  of  the  Solar  Corona, 

coronal  axis  corresponding  to  a  positive  value  of  ft.     (Mini- 
mum of  spots,  1867.5;  maximum,  1870.5.) 

1869,  August  7. 

Both  the  photograph  and  the  drawing  are  in  accord  with  the 
theory.  In  the  drawing  of  MEEK  and  SCHOTT  the  extension  in 
the  equatorial  region  is  greatest  at  the  equator,  while  the  gen- 
eral outlines,  both  in  the  photograph  and  drawing,  are  quite 
similar  to  the  inner  portions  of  Figure  5,  Plate  I.  According 
to  the  boundaries  of  the  wings  as  shown  on  WHIPPLE'S  photo- 
graph, the  axis  of  the  inner  corona  is  inclined  eastward  as 
required  by  theory  when  ft  is  positive.  (Minimum  of  spots, 
1867.5;  maximum,  1870.5.) 

1870,  December  22. 

The  WILLARD  photograph  of  this  eclipse,  aside  from  the  fact 
that  the  polar  rays  and  other  fine  details  of  structure  are  wholly 
wanting,  is  strikingly  similar  to  our  Cayenne  photographs,  when 
they  are  printed  so  as  to  show  only  the  same  extent.  No  fine 
coronal  details  are  shown.  On  the  BROTHERS  photograph  the 
Sun  seems  to  have  reappeared  during  the  exposure.  The  vari- 
ous drawings  of  the  outer  corona  are  discordant  among  them- 
selves. As  required  by  theory,  when  ft  is  negative,  the  wing 
boundaries  indicate  that  the  axis  of  the  inner  corona  is  inclined 
towards  the  west.  (Maximum  of  spots,  1870.5.) 

1871,  December  12. 

The  four  excellent  drawings  by  DAWSON,  give  a  quadrilateral 
outline  to  the  outer  corona,  but  the  others  do  not  as  a  rule  give 
evidence  of  a  small  value  for  ft.  The  photographs  taken  at 
Baikul  and  Dodabetta,  however,  give  almost  exactly  the  same 
detail.  Practically  the  same  structure  is  shown  at  both  poles, 
so  that  a  superficial  inspection  of  the  photographs  alone  will 
not  determine  which  pole  is  turned  towards  the  Earth.  The 
boundaries  of  the  wings  extend  quite  up  to  the  poles,  so  that 
only  the  nearly  normal  rays  at  the  poles  are  shown  on  the  pho- 
tographs. At  the  time  of  this  eclipse,  the  Earth  was  nearer  to 
the  plane  of  the  Sun's  equator  than  it  was  at  any  previous  or 
subsequent  eclipse  of  which  photographs  were  obtained.  Com- 
pared with  the  equatorial  extension,  the  polar  extent  was  very 


By  J.  M.  Schaeberle.  33 

large.  The  observed  general  outline  can,  however,  be  fully  sat- 
isfied by  supposing  the  eruptive  forces  to  have  been  apparently 
more  active  near  the  superior  limits  of  the  Sun-spot  zone,  or 
that  the  equatorial  streamers  suffered  retardation  by  coming 
into  contact  with  returning  streams.  As  the  original  negatives 
were  only  three  tenths  of  an  inch  in  diameter,  considerable 
uncertainty  may  exist  in  the  fainter  outlines  of  the  enlarged 
prints:  I  was  so  fortunate  as  to  have  the  use  of  a  good  positive, 
kindly  loaned  to  me  by  Mrs.  R.  A.  PROCTOR  (evidently  made 
from  a  copy  of  the  original  negative  and  enlarged  about  three 
diameters).  I  made  a  number  of  shorter  timed  negatives,  and 
these  give,  near  the  Sun,  greater  excess  of  equatorial  extent 
and  less  of  polar  extent  than  a  positive  of  the  January  1,  1889, 
eclipse  treated  in  the  same  way,  but  the  boundaries  are  not  as 
sharply  defined  in  the  former  case  as  they  are  in  the  latter. 
From  experiments  with  a  model,  the  forms  of  the  more  lumi- 
nous confused  masses  are  so  plainly  the  result  of  apparent  inter- 
sections of  streamers  (some  of  which  are  doubtless  descending) 
that  a  more  detailed  comparison  can  be  dispensed  with,  since 
no  known  forces  could  possibly  account  for  the  various  forms 
which  can  be  traced  on  this  photograph,  if  we  suppose  the 
observed  outlines  to  represent  actual  forms  in  space.  As 
required  by  the  theory,  the  axis  of  the  inner  corona  is  nearly 
coincident  with  the  Sun's  axis,  being  slightly  inclined  towards 
the  west,  ft  having  a  negative  value.  (Maximum  of  spots, 
1870.5;  minimum,  1879.0.) 

187J,  April  16. 

There  were  no  photographs  taken  at  this  eclipse.  It  is 
described  as  being  similar  to  the  eclipse  of  August,  1868.  As 
drawn  by  STONE,  the  axis  of  the  inner  corona,  given  by  RAN- 
YARD,  is  inclined  towards  the  west,  in  agreement  with  the  typ- 
ical form.  A  mere  drawing,  however,  is  deserving  of  but  little 
weight  so  far  as  the  location  of  this  axis  is  concerned.* 

1875,  April  6. 

This  eclipse  is  described  as  being  curiously  similar  to  the  one 
of  the  previous  year  (April  16).  The  photographs  by  LOCKYER 

*NOTE.— The  observed  data^for  comparison  between  theory  and  observation, 
up  to  and  including  this  date,  have  been  taken  from  RANYARD'S  excellent 
work  on  Solar  Eclipses. 


34        A  Mechanical  Theory  of  the  Solar  Corona, 


and  SCHUSTER  give  unmistakable  evidence  of  a  considerable 
inclination  of  the  Sun's  axis,  as  shown  by  the  boundaries  of  the 
wings.  The  telescopes  were  not  driven  by  clockwork,  so  that 
the  polar  rays  are  not  shown.  The  direction  of  the  Sun's  axis 
is  not  indicated  with  the  necessary  accuracy  to  determine  the 
inclination  of  the  inner  coronal  axis  with  certainty.  (Maxi- 
mum spots,  1870.5;  minimum,  1879.0.) 

1878,  July  29. 

The  first  available  photographs  on  which  the  finer  details  of 
the  structure  at  the  poles  are  of  such  a  character  as  to  permit 
of  their  being  used  to  test  the  correctness  of  the  theory  were 
obtained  at  this  eclipse.  In  the  drawing,  made  by  Professor 
HARKNESS,  from  the  photographs  obtained  at  this  eclipse,  pub- 
lished in  the  volume  issued  by  the  United  States  Naval  Observ- 
atory, the  polar  streamers  are  so  well  defined  that  I  have  been 
able  to  make  the  following  comparison  between  the  observed  (o) 
•and  computed  (c)  values  of  K.  As  the  measures  are  necessa- 
rily only  approximate,  I  have  recorded  the  measured  inclina- 
tions to  the  nearest  five  degrees  for  each  ten  degrees  of  polar 
distance  available: 

1878,  July  29 — Observed  and  Computed  Values  of  K. 


DISTANCES  FROM  NEARER  POLE. 


QUADRANT. 

10° 

20° 

30° 

40° 

0 

c 

0  —  C 

0 

c 

o  —  c 

0 

c 

0  —  C        0 

c 

o—c 

I.  . 

10° 

15° 

—5° 

30° 

31° 

1° 

40° 

46° 

6°     45° 

58° 

13° 

II.  

10 

15 

—5 

15 

31 

16 

35 

46 

—11 

III  

15 

15 

0 

?0 

31 

11 

35 

46 

—  11 

IV  

10 

15 

—5 

"j  

i! 

The  observed  values  in  the  above  table  were  taken  from  the 
composite  drawing  (Plate  XX.,  Fig.  3),  found  in  United  States 
Naval  Observatory  publication  on  the  "  Solar  Eclipse  of  July 
29,  1878."  The  photographs  taken  at  different  stations  are  in 
accord  with  each  other.  The  numerous  drawings  are,  as  usual, 
very  discordant  among  themselves,  but  on  the  whole  indicate 
a  comparatively  large  value  of  ft.  The  northern  wings  have 


By  J.  M.  Schaeberle.  35 

multiple  boundaries  on  the  sides  towards  the  nearer  pole.  Both 
coronal  poles  are  east  of  the  Sun's  poles;  but  the  line  joining 
the  poles  of  the  corona,  as  found  by  means  of  the  boundaries  of 
the  wings  adjacent  to  the  poles,  is  inclined  towards  the  east,  as 
required  for  a  typical  form.  The  polar  rays,  alone  considered, 
wTould  indicate  that  the  coronal  axis  was  nearly  parallel  to  the 
Sun's  axis.  Professor  HARKNESS  calls  attention  to  the  fact  that 
the  orientation  may  be  several  degrees  in  error,  as  only  the 
sides  of  the  photographic  plates  could  be  used  as  guides. 

The  excellent  drawing  by  TROUVELOT  is  in  remarkable  agree- 
ment with  the  photographs.  Naked-eye  drawings  by  Professor 
NEWCOMB  and  Professor  LANGLEY,  the  latter  being  stationed  on 
the  top  of  Pike's  Peak,  show  the  greatest  equatorial  extent  of 
the  corona  that  has  been  observed  up  to  the  present  time. 
(Compare  the  drawing  made  from  the  photographs  with  Figure 
5,  Plate  VI.)  (Minimum  of  spots,  1879.0.) 

1880,  January  11. 

The  sketches  made  during  this  eclipse  show  how  untrustwor- 
thy the  data  derived  from  mere  drawings  can  be.  In  Professor 
DAVIDSON'S  Report  (see  United  States  Coast  and  Geodetic  Sur- 
vey Report  for  1882),  the  corona  is  outlined  as  in  Figure  2  or 
3,  Plate  VI.,  while  in  the  sketches  of  Lieutenant  CHRISTOPHER 
only  a  narrow,  nearly  concentric  band  of  light  is  shown  sur- 
rounding the  dark  limb  of  the  Moon.  There  are  no  photo- 
graphs of  this  eclipse,  so  far  as  known. 

1882,  May  17. 

The  drawing,  made  from  photographs,  given  in  Captain  AB- 
NEY'S  and  Dr.  SCHUSTER'S  report  on  the  solar  eclipse,  is  exceed- 
ingly interesting  as  representing  an  arrangement  of  streamers 
similar  to  the  conditions  found  in  the  model;  that  is,  no  polar 
rays  are  formed.  The  general  appearance  of  the  nearly  circular 
outline  of  the  corona  would  seem  to  indicate  that  the  solar 
activity  was  considerable  in  the  higher  limits  of  the  spot-zones; 
or,  what  is  more  probable,  that  those  in  the  middle  latitudes 
were  retarded,  and  that  the  incoming  streamers  were  more 
numerous  at  the  equator  (see  Postscript),  and  that  in  both 
zones  only  the  more  conspicuous  streamers  of  the  farther  hemi- 
sphere are  seen  in  projection  through  the  dense  masses  of 

4° 


36        A  Mechanical  Theory  of  the  Solar  Corona, 

rays,  most  of  which  are  apparently  wholly  formed  in  the  nearer 
hemisphere.  There  is  strong  evidence  tending  to  show  that 
there  were  numerous  collisions,  as  in  many  places  the  corona 
is  brightest  at  some  distance  from  the  Moon's  outline.  I  can 
almost  exactly  reproduce  this  coronal  form  with  a  model.  The 
inner  portions  of  Figure  2,  Plate  VI.,  are  quite  suggestive. 
(Minimum  of  spots,  1879;  maximum,  1883.) 

1888,  May  6. 

The  drawings  made  by  Professor  TACCHINI  and  Dr.  DIXON  give 
evidence  of  a  considerable  inclination  of  the  Sun's  axis.  The 
Lick  Observatory  does  not  possess  any  photographs. 

Note — October,  1890. — Since  the  above  was  written  the  1889 
volume  of  the  "  Philosophical  Transactions"  has  been  received. 
Like  the  previous  eclipse  (1882)  there  is  much  confusion  in  the 
coronal  detail.  If  the  orientation  of  the  enlarged  drawing  made 
from  photographs  secured  by  the  English  party  is  correct  as 
published  in  this  volume,  then  we  have  here  a  case  of  a  nearly 
circular  corona,  in  which  the  less  inclined  streamers  projected 
near  the  north  pole  of  the  Sun  had  a  decidedly  greater  density 
than  the  more  inclined  ones;  since  the  apparent  north  coronal 
pole  is  at  the  enormous  distance  of  nearly  20°  to  the  east  of  the 
Sun's  pole!!  At  the  south  pole  the  structure  is  more  nearly 
radial,  so  that  the  position  of  the  south  coronal  pole  can  not  be 
located  with  great  accuracy. 

Note  No.  2 — March,  1891. — Since  the  above  has  been  in  type 
I  have,  very  fortunately,  found  a  photographic  print  of  this 
eclipse  (see  Annuaire,  Bureau  des  Longitudes,  1884),  made  by 
M.  JANSSEN  from  a  negative  which  he  exposed  during  the  whole 
time  of  totality.  Although  the  orientation  can  only  be  made 
by  means  of  the  edges  of  the  card  on  which  the  print  is  mounted 
(the  north  pole  is  toward  the  lower  left-hand  corner  of  the 
card),  still  all  doubt  as  to  the  proper  orientation  of  the  above 
mentioned  drawings  seems  to  be  removed.  Dr.  DIXON  observed 
with  a  diagonal  eye-piece;  the  top  of  his  drawing  should  there- 
fore be  marked  S.  instead  of  N. 

In  Mr.  WESLEY'S  drawing  (Phil.  Trans.)  the  top  of  the  page 
is  N.  The  axis  is  correctly  orientated. 

The  remarkable  difference  which  can  exist  between  the  draw- 
yng  of  a  photograph  taken  with  one  instrument  and  a  photo- 
graphic print  from  a  negative  taken  with  another  instrument  is 


By  J.  M.  Schaeberle. 


37 


well  illustrated  in  this  case.  In  JANSSEN'S  print  not  only  are 
the  symmetrical  wings  and  fish  tails  shown,  but  even  the  trumpet- 
shaped  outlines,  on  the  east  side  at  least,  are  unmistakable.  The 
extended  luminosity  near  the  north  pole  would  seem  to  indicate 
that  the  streamers  were  not  uniformly  distributed  in  longitude, 
so  that  the  ratio  of  D  to  D'  is  no  longer  that  which  holds  good  for  a 
typical  corona.  Now,  comparing  Mr.  WESLEY'S  drawing  with 
the  print,  an  apparent  tendency  to  form  two  north  and,  less 
conspicuously,  two  south  coronal  poles  adjacent  to  the  bound- 
aries of  the  wings  is  at  once  recognized.  The  reversal  of  the 
inclinations  near  the  north  pole  is  very  marked  and  is  due  to 
an  irregular  variation  in  the  density  of  the  streamers,  as  can  be 
readily  shown  with  the  aid  of  the  models  (see,  for  instance, 
Plate  VII.,  Fig.  a).  The  tendency  to  form  multiple  poles  is 
also  partially  shown  in  some  of  the  figures  of  Plate  VI. 

The  axis,  which  is  symmetrically  situated  with  reference  to 
these  poles,  in  Mr.  WESLEY'S  drawing,  is  inclined  towards  the 
west,  in  agreement  with  the  theory.  Compare  the  print  with 
Figures  3,  4,  and  6  of  Plate  VI.,  disregarding  the  unsymmetrical 
luminosity  above  the  north  pole.  (Maximum  of  spots,  1883.) 

1886,  August  29. 

The  photographs  taken  by  PICKERING  on  the  Island  of  Gre- 
nada show  enough  of  the  finer  detail  in  certain  places  near  the 
poles  to  allow  of  a  rough  comparison  between  theory  and  obser- 
vation. The  inclinations  (to  the  nearest,  5°)  of  the  polar  rays 
to  normals  through  their  bases  are  given  in  the  table  below  for 
each  10°  of  polar  distance  applicable.  The  measures  are  made 
from  the  drawing  given  in  the  frontispiece  of  Harvard  College 
Observatory  Annals,  Vol.  XVIII.,  No.  V. 


DISTANCE  FROM  NEARER  POLE. 


QUADRANT. 

10° 

20° 

30° 

40° 

o 

c 

0—  C 

0 

c 

o  —  c 

0 

c 

o  —  c 

0 

c 

o  —  c 

I.  . 

15° 

15° 

0° 

25° 

31° 

—  6° 

II. 

15 

15 

0 

20 

31 

—11 

50° 

46° 

4-4° 

Ill; 

10 

15 

—5 

IV. 

? 

38        A  Mechanical  Theory  of  the  Solar  Corona, 


In  the  second  quadrant,  at  30°  polar  distance,  the  rays  are 
not  distinct,  being  nearly  lost  in  the  general  illumination;  the 
measure  is  therefore  unreliable.  Just  at  the  south  pole  there  is 
a  cone  with  the  sides  inclined  10°  to  the  normal,  apparently 
made  by  the  overlapping  of  rays.  On  the  west  side  of  the  north 
pole  the  distribution  of  the  streamers  is  apparently  too  irregu- 
lar to  produce  even  a  trace  of  the  symmetrical  inclined  rays; 
this  supposition  is  further  strengthened  by  the  fact  that  at  25° 
polar  distance  there  is  a  great  wing  extending  to  a  distance 
nearly  equal  to  the  equatorial  extent  of  the  corona.  As  required 
by  the  theory  when  fi  is  positive,  the  axis  of  the  inner  corona 
is  inclined  towards  the  east.  (Maximum  of  spots,  1883;  mini- 
mum, 1888  or  1889.) 

Note — October,  1890. — Since  the  above  was  written  the  volume 
of  the  PhiL  Trans.,  which  contains  a  drawing  of  a  photograph 
of  this  corona  (discussed  by  Messrs.  DARWIN,  SCHUSTER,  and 
MAUNDER),  has  appeared.  The  orientation  differs  something 
less  than  4°  from  the  PICKERING  photograph,  so  that  for  this 
copy  of  the  corona  the  coronal  axis  is  slightly  inclined  west- 
ward. The  following  measures  can  be  compared  with  those  in 
the  preceding  table: 


QUADRANT. 

DISTANCE  FROM  NEARER  POLE. 

10° 

20° 

30° 

40° 

0 

c 

o  —  c 

0 

c 

0  —  C 

0 

c 

o  —  c 

0 

c 

0  —  C 

I.  . 

20° 
20 
10 
0 

15° 
15 
15 
15 

4-5° 

±! 

—15 

40° 
30 
20 
20 

31° 
31 
31 
31 

4-  9° 
—  1 
11 

II  

50° 

46° 

+4° 

III.  .. 

IV  

—11 

If  the  orientation  is  changed  so  as  to  agree  with  PICKERING'S 
diagram,  the  above  residuals  will  be  reduced  in  magnitude  some- 
what. 

1887,  August  18-19. 

The  best  photographs  taken  at  Jourgewetz  by  Dr.  BELOPOLSKY 
are  similar  to  those  of  the  previous  year.  A  certain  con- 
fusion is  apparent,  so  that  no  great  amount  of  detail  is  shown 
at  the  poles.  The.  axis  of  the  inner  corona  apparently  had  a 


By  J.  M.  Schaeberle. 


39 


decided  inclination  toward  the  east,  as  required  by  the  theory 
when  ft  is  positive.  Dr.  GLASENAPP'S  results  give  the  same  evi- 
dence. (Minimum  of  Sun  spots,  probably  1888  or  1889.) 

1889)  January  1. 

It  is  no  exaggeration  to  say  that  the  photographs  taken  dur- 
ing this  eclipse  are  better  than  any  which  had  previously  been 
taken.  On  the  magnificent  negatives  secured  by  BARNARD, 
BURCKHALTER,  CHARROPpiN,  Harvard  College  Observatory 
party,  and  others,  the  coronal  structures  are  shown  in  a  way 
that  leaves  but  little  to  be  desired. 

In  the  following  table  the  comparison  between  theory  and 
observation  will  prove  interesting: 


QUADRANT. 

DISTANCE  FROM  NEARER  POLE. 

10° 

20° 

30° 

40° 

0 

c 

o  —  c 

0 

c 

0  —  C 

0 

c 

0  —  C 

o 

c 

o  —  c 

I 

20° 
20 
10 
10 

15° 
15 
15 
15 

-j-5° 

s 

—5 

30° 

31° 

1° 

35° 

46°  —11° 

50° 

58° 

—8° 

II. 

III. 

25 
25 

31 
31 

—6 
—6 

IV. 

I  have  only  used  those  polar  distances  at  which  the  indi- 
vidual rays  could  still  be  recognized.  The  corona  was  nearly 
of  the  typical  form.  The  great  equatorial  extension  with  the 
trumpet-shaped  outlines  has  just  the  form  which  streamers 
of  indefinite  length  from  low  latitudes  will  produce  in  pro- 
jection. With  the  increase  of  distance  the  illumination 
gradually  fades  out,  but  towards  the  axes  of  greatest  den- 
sity in  projection  the  increasing  number  of  overlapping 
streamers  causes  a  gradual  increase  in  the  illumination,  result- 
ing in  the  trumpet-shaped  outlines  which  form  so  promi- 
nent a  feature  of  this  eclipse.  For  all  coronas,  in  which  the 
fish  tails  are  prominent,  this  particular  feature  should  here- 
after be  shown  in  cases  where  the  observers  are  favored  with 
exceptionally  good  atmospheric  conditions.  This  was  the  case 
for  the  present  eclipse;  the  clear  California  sky  revealed  out- 
lines not  before  seen  on  photographs  taken  during  sun-spot 
minima. 


40        A  Mechanical  Theory  of  the  Solar  Corona, 


Not  only  is  this  phenomenon  a  necessary  consequence  of  the 
theory,  but  all  doubt  as  to  its  nature  would  seem  to  be  removed 
by  the  appearance  of  the  photographs  themselves;  numerous 
streamers,  of  such  a  length  and  form  as  to  preclude  the  idea 
that  they  coincide  with  magnetic  lines  of  force,  are  seen  radiat- 
ing from  parts  of  the  Sun's  limb,  which  indicate  that  the 
origins  are  in  the  low  latitudes.  Here,  again,  the  model  need 
only  be  compared  with  the  photographs,  to  test  the  agreement 
of  the  theory  with  observation.  The  boundaries  of  the  wings 
in  the  southern  hemisphere  are  multiple  on  the  sides  turned 
toward  the  nearer  pole.  The  axis  of  the  inner  corona,  as 
required  by  the  typical  form,  is  inclined  toward  the  west,  the 
Earth  being  below  the  Sun's  equator.  (Minimum  of  spots, 
1888  or  1889.) 

1889,  December  21,  22. 

The  photographs  taken  at  Cayenne  again  show  the  structure 
of  the  corona  with  such  minuteness  of  detail  that  a  direct  com- 
parison between  the  observed  and  theoretical  inclinations  of  the 
polar  rays  can  also  be  used  to  test  the  theory. 

As  the  position  of  the  meridian  is  not  indicated  on  the  prints, 
the  photographs  can  be  accurately  orientated  by  means  of  the 
following  datum.  The  center  of  the  heaviest  north  polar  ray 
(the  most  westerly  one  of  the  more  conspicuous  and  nearly 
normal  rays)  has  a  position  angle  of  4°. 8;  the  pole  of  the  Sim 
is  therefore  2°  east  of  the  heavy  north  polar  ray. 


DISTANCE  FROM  NEARER  POLE. 


QUADRANT. 

10° 

20° 

30° 

40° 

0 

c 

o  —  c 

0 

o—c 

0 

c 

0  —  C 

0 

c 

o  —  c 

I. 

10° 

15° 

—5° 

20° 

31° 

—11° 

40° 

46° 

—  6° 

11.  ... 

10 

16 

—5 

III.  .. 

9,0 

15 

4-5 

25 

31 

—  6 

45 

46 

i 

IV  

20 

15 

+5 

35 

81 

-h  4 

45 

46 

_1 

Although  the  sky  was  apparently  free  from  clouds  during  the 
total  phase  of  the  eclipse,  the  air  was  so  charged  with  moisture 
that  the  atmospheric  glare  must  have  been  very  prominent. 
Yet,  notwithstanding  these  conditions,  the  equatorial  extent  of 
the  corona,  as  shown  on  the  photographs,  is  more  than  a  degree; 


By  J.  M.  Schaeberle.  41 

the  wings  are  very  conspicuous,  and  the  polar  rays  are  shown 
with  all  desired  distinctness.  The  trumpet- shaped  outlines,  so 
prominent  a  feature  in  the  previous  eclipse,  are  lost  in  the  sky 
illumination,  although  faint  traces  of  this  phenomenon  can  be 
distinguished. 

In  the  southern  zone  there  was  evidently  a  vigorous  outburst 
near  longitude  r — r0=0°.  The  protuberances  (shown  on  the 
negatives)  projected  at  this  part  of  the  Moon's  outline  give 
evidence  to  the  same  effect.  The  boundaries  of  the  wings  in 
the  southern  hemisphere  are  multiple  on  the  sides  turned 
towards  the  nearer  pole. 

As  required  by  the  theory,  the  axis  of  the  inner  corona  is 
inclined  slightly  towards  the  west,  the  Earth  being  below  the 
Sun's  equator.  (Minimum  of  spots,  1888  or  1889.) 

Probable  Form  of  the  Solar  Coronas  of  1892  and  1893. 

The  next  total  eclipse  of  the  Sun  takes  place  in  1892,  April 
26.  If  observed,  the  following  prediction  as  to  its  form  should, 
in  general,  be  verified,  under  favorable  atmospheric  conditions: 
Polar  extent  large.  Inner  coronal  axis  (if  polar  rays  or 
wings  are  shown)  inclined  westward.  Rifts  numerous.  Indi- 
cations of  collisions.  General  form  similar  to  Figure  7,  Plate 
VI.  The  same  description  will  apply  to  the  eclipse  of  April 
15-16,  1893. 

It  will  be  noticed  that  I  have  used  the  same  constants  for 
finding  the  value  of  Jc  for  a  given  p  in  all  cases  (see  page  75). 
A  closer  agreement  between  theory  and  observation  could  doubt- 
less have  been  obtained  by' varying  the  values  of  c  and  a  (for 
different  values  of  /?)  and  taking  into  account  the  shifting  of  the 
coronal  pole;  but  as  it  appeared  that  the  measured  inclinations 
were  liable  to  errors,  which  as  a  rule  much  exceeded  those  due  to 
neglecting  the  terms  which  involved  or  caused  the  shifting  of 
the  coronal  poles,  I  deemed  it  best  to  refer  all  measures  to  the 
Sun's  true  poles.  The  magnitude  of  the  residuals  obtained  can 
then  be  used  to  detect  any  abnormal  discrepancies  which  may 
result  from  some  error  in  the  orientation  of  the  photograph. 

The  object  of  the  present  investigation  was  not  to  force  an 
exact  agreement  by  the  arbitrary  variation  of  certain  quanti- 
ties, but  to  secure  confirmatory  or  non-confirmatory  evidence, 


42        A  Mechanical  Theory  of  the  Solar  Corona, 

by  comparing  a  purely  theoretical  investigation  of  a  general 
character  with  the  results  obtained  from  actual  observation. 

It  is  hardly  necessary  to  state  that  nothing  in  this  theory 
requires  that  all  the  streamers  shall  be  confined  between  any 
fixed  circles  of  latitude,  nor  that  the  apparent  density  and 
magnitude  of  the  streamers  may  not  be  subject  to  periodic 
variations,  due  to  physical  causes  which  relate  to  the  molecular 
nature  of  the  Sun's  internal  constitution,  with  which  this  in- 
vestigation has  nothing  to  do.  (See  Postscript.) 

There  seems  to  be  no  feature  of  the  coronal  structure  which 
cannot  be  accounted  for  in  a  satisfactory  manner  by  this  new  theory 
of  the  solar  corona. 

In  conclusion,  it  gives  me  pleasure  to  thank  Messrs.  BURN- 
HAM  and  BARNARD  for  their  aid  in  the  work  of  the  photographic 
reproductions,  and  Mr.  KEELER  for  various  information  relating 
to  spectroscopic  solar  physics. 

I  am  much  indebted  to  Professor  HOLDEN,  who,  during  the 
preparation  of  this  memoir,  has  ever  been  ready  to  aid  me  in 
various  ways. 

MT.  HAMILTON,  June,  1890. 

J.  M.  SCHAEBERLE. 


POSTSCRIPT. 

I  have  spent  some  time  in  an  extended  examination  of  the 
magnificent  spectroscopic  observations  made  at  Rome,  with  a 
view  to  determine,  if  possible,  whether  the  solar  prominences 
observed  in  high  latitudes  could  not  be  reconciled  to  the  hypoth- 
esis that  they  were  but  the  projections  of  streams,  which,  issu- 
ing from  a  low  latitude,  appeared  in  projection  to  come  from 
the  limb  of  the  Sun.  In  many  instances  this  seems  to  be  the 
case,  but  the  complications,  especially  in  the  low  latitudes, 
resulting  from  the  perspective  overlapping  of  these  promi- 
nences in  largely  different  longitudes,  is  so  great  that  much 
uncertainty  exists  as  to  the  motion  of  any  given  prominence. 
The  uncertainty  could  be  settled  at  once  by  following  a  con- 
spicuous polar  prominence  for  several  hours,  and  carefully 
recording  its  position-angle  from  time  to  time.  If  the  base  of 
such  a  prominence  is  in  a  low  latitude,  the  position-angle 


By  J.  M.  Schaeberle.  43 

should  change  at  the  rate  of  about  2°  an  hour.  I  have  not 
had  an  opportunity  to  make  an  observation  of  this  kind  since 
the  theoretical  investigation  was  completed. 

The  prominences  at  the  poles  are  so  rare,  and  the  observa- 
tions usually  so  short,  that  no  definite  conclusions  can  be  drawn 
from  the  data  at  hand.  Again,  prominences  at  the  poles  should, 
on  this  hypothesis,  always  have  large  component  velocities  either 
towards  or  away  from  the  Earth. 

During  the  total  eclipse  of  August  29,  1886,  Professor  SCHUS- 
TER observed  the  spectrum  of  a  great  prominence  near  the  pole 
of  the  Sun.  His  observations  indicated  a  motion  of  two  hun- 
dred and  forty-seven  miles  per  second  towards  the  observer. 
Assuming  the  origin  of  the  prominence  to  be  in  the  spot-zone, 
this  velocity  indicates  roughly  an  initial  parabolic  velocity. 

As  bearing  upon  this  point,  th'e  following  extracts  from 
"  Chemistry  of  the  Sun,"  by  that  eminent  solar  physicist,  J. 
NORMAN  LOCKYER,  will  be  found  very  suggestive.  The  italics 
are  my  own:  . 

Such  prominences  have  been  seen  to  mount  upwards  at  the  rate  of  250 
miles  a  second  ;  that  is,  nearly  1,000,000  miles  an  hour.  *  *  *  There 
are  indications  that  these  prominences,  instead  of  rising  vertically,  as  we  may 
imagine  them  to  do,  are  at  times  shot  out  sideways — almost  tangentially.  In  that 
case,  of  course,  the  spectroscope  enables  us  to  determine  the  velocity.  One 
hundred  miles  a  second,  either  towards  or  from  the  eye,  is  by  no  means  an  uncommon 
velocity.  *  *  *  The  height  of  some  of  these  prominences  is  very  great. 
Professor  YoiTNG  records  one  seen  in  1878  as  being  nearly  400,000  miles  high  ; 
that  is,  13^  minutes  of  arc,  the  solar  radius  being  16  minutes. 

The  actual  velocity  of  motion  will,  in  general,  always  be 
greater  than  the  observed,  since  the  spectroscope  only  gives 
that  component  which  is  parallel  to  the  Earth's  radius-vector, 
while  the  direct  visual  observation  only  gives  the  component 
at  right  angles  to  the  same  line. 

The  small  inclined  saw-tooth  protuberances,  as  well  as  many 
of  the  grotesque  larger  ones,  are  probably  formed  in  much  the 
same  way  that  the  polar  rays  are  produced;  the  sudden  changes 
of  inclination  being  due  to  variations  in  the  density  of  the 
streams.  It  would  seem  to  require  a  continuous  and  more  or 
less  uniform  series  of  eruptions  in  certain  zones  on  the  solar 
surface  to  satisfactorily  account  for  these  ever-present  smaller 
protuberances,  and  the  theory  certainly  demands  such  a  dis- 
tribution of  the  streamers.  Let  us  now  consider 


44        A  Mechanical  Theory  of  the  Solar  Corona, 


SOME   PHYSICAL   PHENOMENA    INVOLVED    IN    THE    MECHANICAL 
THEORY  OF  THE  CORONA. 

While  I  invite  the  severest  criticism,  from  astronomers,  of  the 
theory  given  in  the  preceding  pages,  I  ask  their  indulgence  with 
reference  to  certain  deductions  which  I  have  made,  and  now, 
with  great  deference,  submit  to  their  attention.  Assuming  my 
premises  (The  Mechanical  Theory)  to  be  true,  I  trust  that  in 
deducing  some  of  the  resulting  phenomena  my  arguments  will 
at  least  be  found  to  have  a  logical  sequence. 

All  the  results  obtained  in  the  foregoing  investigation  have 
been  deduced  on  the  hypothesis  that  the  force  of  ejection  is 
such  as  to  give  a  parabolic  velocity  to  the  streams;  but  so  far 
as  the  form  near  the  Sun  is  concerned,  an  inspection  of  Table  I. 
at  once  shows  that  practically  the  same  results  would  be  obtained 
on  the  hypothesis  that  the  force  is  only  just  sufficient  to  give  an 
elliptical  velocity  corresponding  to  a  period  of  only  a  few  hours. 

The  moment  the  returning  streams  are  taken  into  consider- 
ation the  effect  is  such  as  to  cause  a  periodic  variation  in  the 
detail  of  the  corona,  and  simultaneously  to  cause  a  periodic  vari- 
ation in  the  surface  features  of  the  Sun,  as  I  shall  now  proceed 
to  show. 

To  whatever  cause  the  eruptions  in  certain  zones  on  the 
Sun  may  be  due,  we  are  evidently  justified  in  assuming  that, 
in  the  long  run,  the  forces  there  at  work  have,  at  a  given  period 
of  the  Sun's  age,  a  mean  value  (F).  One  measure  of  this  force 
(F)  will  be  the  maximum  distance  (d)  from  the  Sun's  center 
(=2a  nearly),  to  which  a  given  particle  (mass=m)  is  projected 
in  the  time  \t  (nearly),  so  that  the  periodic  time  will  be  t.  As 
has  already  been  shown,  the  heliocentric  latitude  of  an  ejected 
particle  during  its  whole  motion  will  remain  nearly  the  same, 
so  that  the  latitudes  of  different  parts  of  the  same  stream  will 
be  nearly  the  same  as  the  latitude  of  the  point  of  ejection.  Now, 
if  each  stream  of  particles  in  a  given  zone  is  ejected  by  an 
instantaneous  force  (F),  the  more  advanced  portions  of  the 
streams  will  be  unimpeded  during  the  first  half  of  their  path ; 
on  returning,  however,  the  chance  of  collision  with  the  same  or 
other  outgoing  streams  varies  inversely  as  the  square  of  the 
distance  from  the  Sun. 

Near  the  Sun,  therefore,  collisions  must  occur  which  tend  to 


By  J.  M.  Schaeberle.  45 

retard  or  stop  the  outgoing  streams,  resulting  in  a  temporary 
increase  in  the  heat  of  the  combined  colliding  masses  (causing 
a  consequent  increase  in  the  brightness  of  the  corona  at  such 
places,  and  at  the  same  time  rendering  the  coronal  detail  more 
confused).  This  heat  will  tend  to  be  largely  dissipated  before 
such  masses  fall  back  into  the  Sun,  which  they  will  then  reach 
with  comparatively  small  velocity  and  low  temperature.  Unre- 
tarded  returning  streams  on  striking  the  Sun  will  tend  to  greatly 
raise  the  temperature  at  the  points  of  impact;  perturbed  return- 
ing streams  could,  of  course,  strike  all  parts  of  the  Sun's  surface, 
but  the  general  tendency  of  these  perturbations  will  be  to  dimin- 
ish the  latitudes  of  the  returning  streams.  Unperturbed  return- 
ing streams  will  always  fall  within  the  limits  of  the  Sun-spot 
zones. 

So  long  as  the  incoming  streams  are  very  numerous,  the  out- 
going ones  will,  in  a  great  measure,  be  stopped,  so  that,  after 
the  interval  t,  there  will  be  comparatively  few  returning  streams; 
a  direct  consequence  of  this  state  of  things  is  to  allow  free  pas- 
sage for  the  outgoing  streams,  which,  since  there  are  now  but 
few  collisions,  results  in  (1)  an  apparent  diminution  in  the 
brightness  of  the  corona,  (2)  more  regular  and  sharply  defined 
detail,  and  (3),  in  general,  a  more  uniformly  illuminated  solar 
surface  (i.  e.,  fewer  solar  spots). 

The  periodic  character  of  this  phenomenon  can  be  well  illus- 
trated by  means  of  a  vertical  jet  of  water.  When  the  water  is 
first  turned  on  it  almost  instantly  shoots  up  to  its  maximum 
height;  the  returning  drops  then  gradually  check  the  velocity 
of  the  stream  near  the  origin,  so  that  after  a  moment  the  whole 
mass  seems  to  be  piled  up  just  a  little  above  the  orifice;  before 
the  last  portions  of  the  still  falling  stream  reach  the  retarded 
stream  the  jet  begins  to  resume  its  former  activity,  and  then 
again  rises  to  a  considerable  height.  These  oscillations  are 
repeated  at  nearly  uniform  intervals,  the  period  of  one  complete 
phase  being  roughly  equal  to  twice  the  time  required  for  a  given 
drop  to  describe  the  whole  path. 

If  the  ejective  force  is  such  as  to  make  t  about  five  years,  a 
complete  cycle  of  changes  will  take  place  in  the  time  2t,  and 
after  the  same  manner  as  is  observed  in  the  Sun-spot  cycle.  It 
is  rather  remarkable  that  the  aphelion  distance  of  the  streams 
corresponding  to  this  value  of  t  is  nearly  the  same  as  Jupiter's 


46        A  Mechanical  Theory  of  the  Solar  Corona, 

distance  from  the  Sun;  so  that  the  perturbations  produced  by 
this  planet  may  have  more  to  do  with  the  regularity  of  the 
period  than  the  assumed  constant  force  of  ejection.  The  initial 
velocity  required  to  just  carry  a  particle  from  the  Sun  to  Jupiter 
is  but  little  less  than  a  parabolic  velocity.  For  an  initial  para- 
bolic velocity  Saturn,  alone  considered,  would,  on  the  same 
hypothesis,  cause  a  complete  cycle  of  less  marked  changes  in 
twenty  years,  Uranus  in  sixty  years,  and  Neptune  in  one  hun- 
dred and  twenty  years.  The  comparatively  insignificant  plan- 
ets inside  of  the  orbit  of  Jupiter  would  cause  minor  variations, 
corresponding  to  cycles,  which,  even  for  Mars,  would  be  of  less 
than  two  years'  duration. 

A  maximum  of  Sun  spots  will  therefore  correspond  to  the 
times  when  the  returning  streams  are  most  numerous;  the 
corona  at  these  same  times  will  be  brightest  and  most  con- 
fused near  the  Sun,  and  on  account  of  the  retardations,  the 
equatorial  extent  will,  as  a  rule,  be  least.  But  at  the  equator 
there  will  be  more  returning  than  outgoing  streams  (on  account 
of  the  planetary  perturbations)  ;  consequently,  the  illumination 
in  this  plane  will  be  greater  at  this  time  than  it  is  when  only 
outgoing  streams  are  present. 

A  minimum  of  Sun  spots  will  correspond  to  the  times  when 
the  incoming  streams  have  been  exhausted.  Consequently, 
the  unimpeded  outgoing  streams  will  have  their  normal  veloc- 
ity and  extent,  the  corona  will  show  great  equatorial  extension, 
and,  as  a  rule,  be  more  sharply  defined  and  have  more  promi- 
nent fish-tail  outlines,  especially  when  the  Earth  is  near  the 
Sun's  equator. 

In  the  equation: 


V  increases  as  M  diminishes.  As  it  is  probable  that  at  the 
instant  of  ejection  the  masses  are  of  a  gaseous  character,  the 
velocity  may  be  very  great  without  necessarily  requiring  an 
improbable  ejective  force.  It  may  be  well  to  call  attention  to 
the  fact  that  the  initial  velocity  required  to  send  a  particle  to  a 
distance  of  only  one  solar  diameter  from  the  Sun's  surface  is 
already  greater  than  four  fifths  of  the  velocity  required  to  send 
the  same  particle  to  an  infinite  distance.  For  lines  of  motion 


By  J.  M.  Schaeberle.  47 

which  are  not  normal  to  the  Sun's  surface,  much  greater  initial 
velocities  will  be  required  to  carry  the  particles  to  the  same 
distance. 

On  this  hypothesis  the  duration  of  the  Sun-spot  period  there- 
fore indicates  that  the  forces  of  ejection  are  such  as  to  give  the 
streams  a  mean  velocity  but  little  less  than  that  in  a  parabolic 
orbit.  Streamers  having  inclined  initial  directions  of  motion 
will,  as  a  rule,  either  be  destroyed  by  others,  or  be  so  scattered 
that  no  marked  effects  will  be  produced  by  them.  (The  zone 
of  maximum  Sun  spots  is  the  same  as  the  zone  above  which  the 
maximum  number  of  collisions  takes  place.)  As  the  Earth's 
maximum  distance  from  the  plane  of  the  Sun's  equator  is  less 
than  8°,  and  as  the  zone  of  maximum  activity  on  the  Sun  has 
twice  this  latitude,  the  chance  of  the  Earth  passing  through 
an  outgoing  stream  is  less  than  it  is  for  an  incoming  (perturbed) 
stream.  Such  encounters  must,  however,  take  place. 

THE  ZODIACAL  LIGHT  AND  THE  GEGENSCHEIN. 

According  to  the  Mechanical  Theory,  the  ejected  streams  of 
matter,  although  they  are  of  double  curvature,  will  always  be 
directed  nearly  towards  the  Sun  (except  at  aphelion).  Let  us 
now  consider  some  phenomena  which  can  be  produced  experi- 
mentally. The  diffused  light  caused  by  a  series  of  nearly 
parallel  luminous  lines  (of  indefinite  extent)  very  distant  from 
the  observer  will  always  be  most  conspicuous  in  those  direc- 
tions in  which  the  lines  are  projected  as  mere  points.  If  the 
observer  is  placed  within  the  space  through  which  these  lines 
pass,  there  will  be  two  points  of  equal  maxima  180°  apart; 
but  if  the  actual  intrinsic  brilliancy  of  the  lines  increases 
from  one  extremity  of  the  set  to  the  other,  then,  of  course,  the 
two  maxima  will  differ  enormously  in  brilliancy.  If  the  depth 
of  these  lines  in  cross-section  is  the  same  on  all  sides  of  the 
observer,  the  illumination  will  be  symmetrically  arranged  in 
concentric  zones,  which  gradually  decrease  in  brightness  as  the 
angular  distance  from  their  common  pole  (which  corresponds 
to  the  brighter  maximum)  increases,  until  the  angular  distance 
is  reached  at  which  the  apparent  increase  in  brilliancy  due  to 
projection  more  than  compensates  for  the  decrease  in  brilliancy 
due  to  distance  from  the  origin.  If  one  diameter  of  the  cross- 
section  at  the  observer  is  greater  than  any  other,  the  excess  in 
depth  produces  an  apparent  increase  of  illumination  in  a  plane 


48       A  Mechanical  Theory  of  the  Solar  Corona, 

which  contains  this  diameter  and  the  vanishing  points  of  the 
lines,  the  law  of  variation  of  brightness  in  this  plane  being  the 
same  as  for  a  circular  cross-section.  If  the  observer  is  near, 
but  not  within,  the  space  traversed  by  the  lines  of  indefinite 
extent,  no  conspicuous  variations  will  be  apparent,  although 
one  hemisphere  will  actually  be  brighter  than  the  other.  If 
in  each  of  the  above  cases  the  luminous  lines  be  assumed  to 
radiate  from  a  common  center,  which  is  at  a  great  distance  from 
the  point  of  observation,  the  distribution  of  those  lines  which 
pass  nearest  to  the  observer  will,  on  account  of  their  small 
distance,  almost  wholly  determine  the  form  of  the  resulting 
phenomenon. 

Let  us  now  consider  the  phenomenon  caused  by  the  outgoing 
and  incoming  streamers  from  the  Sun.  In  December  and  June 
the  Earth  is  in  the  plane  of  the  Sun's  equator  and  at  its  maxi- 
mum distance  from  the  nearest  zone  of  streamers,  and  it  is 
symmetrically  situated  with  reference  to  both  zones.  Now, 
since  the  Earth  is  in  neither  of  these  zones,  no  great  contrasts 
of  light  will  be  produced  on  the  side  opposite  to  the  Sun.  Even 
if  there  were  no  streamers  near  the  Earth,  the  light  in  the 
two  hemispheres  would  be  so  diffused  (covering  the  whole  visible 
sky  with  the  exception  of  an  ill-defined  less  luminous  band 
along  the  ecliptic)  that  it  is  quite  probable  the  variations  in 
light  would  not  be  apparent,  except  at  the  time  of  an  eclipse  of 
the  Sun,  when  typical  coronal  forms  would  be  seen.  But  the 
arrangement  of  the  comparatively  few  streamers  which  pass 
near  the  Earth  on  all  sides  will,  on  account  of  their  nearness, 
now  determine  the  resulting  form  of  the  outlines.  The  density 
in  projection  will  evidently  be  greatest  in  the  plane  of  the  Sun's 
equator,  but  this  density  will  be  at  a  minimum. 

When  the  Earth  is  at  its  greatest  distance  above  (September) 
or  below  (March)  the  plane  of  the  Sun's  equator,  it  will  be  at 
its  least  distance  from  the  zone  of  maximum  density  of  the 
streamers.  In  projection,  the  density  will  now  be  greatest  in 
a  plane  which  is  practically  coincident  with  the  plane  of  the 
ecliptic;  the  excess  of  streamers  in  the  direction  of  maximum 
density  will,  however,  have  a  tendency  to  cause  the  center  of 
illumination  to  be  shifted  slightly  above  the  plane  of  the  ecliptic 
in  March  and  slightly  below  this  plane  in  September.  (The  effect 
of  the  decrease  in  latitude  of  the  returning  streams  will  have  a 
precisely  similar  tendency.)  In  general,  at  any  time  of  the  year, 


By  J.  M.  Schaeberle. 


49 


the  illumination  at  any  angular  distance  from  the  Sun  will  be 
greatest  near  a  plane  which  contains  the  radius-vector  of  the  Earth, 
and  which  is  perpendicular  to  the  orthographic  projection  of  the 
Sun's  axis. 

The  phenomenon  will  be  least  conspicuous  in  December  and 
June,  and  most  conspicuous  in  September  and  March.  It  will 
always  be  brightest  near  the  Sun,  and  gradually  diminish  in 
intensity  to  within  a  certain  distance  of  the  point  which  is 
180°  from  the  Sun,  where  theoretically  there  will  be  a  slight 
increase  in  the  luminosity.  These  conditions  are  in  agreement 
with  actual  observation. 

Now,  the  effect  of  the  perturbations  of  the  superior  planets  is 
always  such  that  the  latitude  of  a  normally  ejected  returning 
stream  will  be  less  than  that  of  the  same  outgoing  stream;  con- 
sequently, these  streams  will  be  more  conspicuous  to  an  observer 
in  a  smaller  heliocentric  latitude  than  the  outgoing  streams.  If 
lines  are  drawn  from  the  Earth  tangent  to  the  incoming  stream, 
these  lines  will.aM  have  a  slightly  less  longitude  than  that  of 
the  Earth,  so  that  the  center  of  the  secondary  maximum  will 
always  be  west  of  the  point  which  is  180°  from  the  Sun,  if  the 
returning  stream  is  more  conspicuous  than  the  outgoing  one, 
since  lines  from  the  Earth  drawn  tangent  to  the  outgoing  stream 
will  always  lie  east  of  the  same  point.  The  greatest  extent  will 
be  in  longitude. 

To  show  how  this  theory  agrees  with  observation,  I  give  be- 
low a  resume  of  the  published  results  of  the  most  noted 
observers  of  the  Gegenschein.  I  have  taken  the  mean  results 
for  two  series,  one  corresponding  to  the  months  when  the  Earth 
was  above  the  Sun's  equator,  the  other  when  it  was  below  this 
plane: 


ow2 

si 

^ 

g 

Teriod. 

pa 

|| 

If 
11 

2, 

Observers. 

Reference. 

||| 

2.2, 

CD  0 

s 

Mar.  to  April 

+1-.9 

-1°.5 



12 

•    SCHMIDT  _. 

..  Astr. 

Aug.  to  ISov. 
Feb.  to  May. 

+2.1 
0.0 

+0  .2 
—2.0 

i 

33 
32 

SEARLE  & 

Nach.,No.l726. 

Aug.  to  Oct.. 

—0.2 

+0.2 

+ 

11 

I"  WENDELL.. 

...Astr.  Nach., 
Nos.  2376-2441. 

Sept.  to  Oct.  . 

+2.8 

—0.7 

— 

4 

[•  BARNARD  . 

Astr.  Jour- 

Feb. to  Mar. 

+0  .1 

+0.8 

+ 

11 

nal,    No.     168. 

50       A  Mechanical  Theory  of  the  Solar  Corona, 

While  the  individual  observations  on  any  given  day  are 
often  very  discordant,  the  above  mean  results  certainly  show  a 
remarkable  agreement  with  the  theory. 

When  one  considers  that  the  area  covered  by  the  Gegenschein 
is  often  as  much  as  20°  long  by  10°  or  15°  wide,  the  difficulty 
of  accurately  locating  the  center  of  such  a  faint  object,  the 
caution  with  which  apparently  confirmatory  evidence  should 
be  regarded,  can  be  better  understood. 

In  any  given  latitude  the  effect  of  differential  atmospheric 
absorption  of  light  will  always  have  a  tendency  to  apparently 
shift  the  center  of  illumination  towards  the  zenith  of  the  place. 
In  northern  latitudes  (greater  than  23°.5)  the  apparent  dis- 
placement due  to  atmospheric  absorption  will  always  be  greater 
in  June  than  in  December,  and  about  the  same  in  March  and 
September. 

Since  there  appears  to  be  no  marked  parallax  for  the  Gegen- 
schein, and  since  the  absence  of  strong  solar  light  within  the 
Earth's  shadow  appears  to  have  no  sensible  effect  on  the  central 
portions  of  this  illumination,  it  follows  that  much  the  greater 
portion  of  the  matter  composing  the  streams  must  be  much 
farther  away  from  the  Earth  than  the  length  of  the  Earth's 
shadow. 

Further  observations,  and  a  much  more  extended  comparison 
between  theory  and  existing  observations,  are  of  course  neces- 
sary before  definite  conclusions  can  be  drawn.  In  a  general 
way,  however,  I  have,  as  it  appears  to  me,  conclusively  shown 
that  a  phenomenon  similar  in  form  and  position  to  the 
observed  Zodiacal  Light  and  Gegenschein  must  necessarily  be 
produced  by  ejected  particles  whose  orbits  have  a  major  axis 
greater  than  the  Earth's  radiusrvector  and  whose  theoretical 
perihelion  is  near  the  Sun's  center. 

FORWARD  DRIFT  OF  THE  SOLAR  SURFACE. 

The  planetary  perturbations  in  longitude  will  always  be  such, 
that  while  the  eccentricity  of  the  orbits  of  some  of  the  particles 
will  be  increased  (even  to  the  extent  of  causing  a  retrograde 
motion),  by  far  the  greater  number,  especially  those  having 
small  latitudes,  will  become  less  eccentric,  so  that  the  resultant 
effect  is  to  cause  the  returning  masses  to  strike  the  Sun  with  a 


By  J.  M.  Schaeberle.  51 

greater  angular  velocity  than  that  of  the  Sun's  surface,  thus 
causing  an  actual  forward  drift  of  this  surface,  which  will  be 
greatest  in  the  Sun's  equatorial  regions,  in  agreement  with  ob- 
servation. (A  variation  in  the  angular  distance  of  the  Gegen- 
schein  from  the  Earth's  radius- vector  produced  is  also  a  function 
of  the  planetary  perturbations  in  longitude.) 

TERRESTRIAL  MAGNETISM. 

We  know  from  actual  observation  that  the  atmosphere  of  our 
planet  is  continually  bombarded  by  meteoric  matter,  which  is 
often  volatilized  before  it  reaches  the  Earth's  surface.  If  we 
imagine  the  Earth  to  be  in  the  center  of  a  stream  of  uniformly 
distributed  matter  having  a  rectilinear  motion  in  a  given  direc- 
tion, it  is  at  once  evident  that  owing  to  the  rotation  of  the  Earth 
the  maximum  amount  of  meteoric  matter  will  fall  at  the  place 
which  has  the  least  linear  velocity  for  a  given  inclination  of 
the  local  horizon  to  the  direction  of  the  stream's  motion,  so  that 
at  the  equator  the  amount  of  matter  per  unit  of  the  area  will 
be  at  a  minimum,  while  a  very  decided  maximum  will  be  at 
each  pole.  Even  for  the  case  when  the  path  of  the  stream  is 
parallel  to  the  Earth's  equator,  the  area  about  the  poles  will,  on 
account  of  the  Earth's  mass,  still  receive  more  foreign  matter 
than  a  corresponding  area  nearer  the  equator,  since  particles 
will  not  only  be  deflected  from  the  more  distant  portions  of  the 
stream  so  as  to  strike  the  areas  near  the  poles,  but  the  new  instan- 
taneous orbits  described  by  these  more  distant  particles  will  be 
such  that  even  the  region  beyond  the  poles  will  be  bombarded. 
If  either  pole  is  inclined  towards  the  direction  from  which  the 
stream  is  coming,  the  amount  of  matter  received  at  that  pole 
will  be  enormously  greater  than  it  will  for  a  corresponding  area 
at  the  equator.  If  the  surface  on  which  the  matter  falls  is  per- 
manent, there  will  be  a  continual  accumulation  of  such  matter; 
if,  on  the  other  hand,  the  surface  is  a  movable  one,  like  water 
or  a  moving  field  of  ice,  the  matter  does  not  necessarily  accu- 
mulate at  the  place,  since  ocean  currents,  sooner  or  later,  will 
cause  a  general  distribution  over  the  globe. 

Now,  if  we  look  at  a  map  of  the  Earth,  we.  find  that,  beyond  a 
certain  distance,  the  north  pole  is  almost  completely  surrounded 
by  land;  the  Arctic  Ocean  bounds  the  northern  coast  of  Europe, 
5s 


52        A  Mechanical  Theory  of  the  Solar  Corona, 

Asia,  and  Alaska.  But  from  Eastern  British  America  towards 
the  pole  the  whole  area  is  practically  land-locked,  so  that  this 
area  will  contain  the  greatest  amount  of  accumulated  meteoric 
matter.  The  most  northerly  portions  of  Siberia  will  come  next 
in  order.  At  the  south  pole  practically  the  whole  Antarctic 
region  is  still  unexplored;  but  while  the  areas  of  maximum 
amount  of  accumulated  matter  cannot  be  accurately  located,  it 
is  at  once  evident  that  the  total  area  over  which  the  mass  of 
meteoric  matter  can  accumulate  will  be  much  greater  in  the 
Northern  than  in  the  Southern  Hemisphere. 

Now,  the  larger  meteoric  masses  which  reach  the  Earth's  sur- 
face are  found,  on  examination,  to  be  strongly  magnetic,  and 
the  smaller  masses  are  undoubtedly  magnetic  also.  Hence,  the 
arrangement  of  individual  meteoric  particles  covering  a  given 
surface  will  be  such  that  each  one  naturally  assumes  a  fixed 
position  with  reference  to  the  resultant  lines  of  magnetic  force. 
Of  the  two  poles  formed,  the  one  in  the  Antarctic  region  will 
(in  agreement  with  observation)  show  the  greatest  force,  since 
the  space  into  which  the  lines  of  force  are  condensed  will  be 
least  in  the  Southern  Hemisphere.  As  is  also  well  known  from 
actual  observation,  there  are  two  areas  or  centers  of  maximum 
force  near  each  magnetic  pole;  at  least  such  is  the  case  for  the 
Northern  Hemisphere,  where  the  area  of  greater  maximum  of 
force  is  in  Northern  British  America,  while  the  lesser  maximum 
is  in  Northern  Siberia.  A  possible  shifting  of  the  immense  ice 
fields  at  both  poles,  of  course  involves  a  corresponding  move- 
ment of  the  meteoric  matter  imbedded  in  these  fields,  and  a 
consequent  shifting  of  the  centers  of  force  results.  The  direc- 
tion of  the  Earth's  magnetic  lines  of  force  should,  according 
to  this  theory,  be  largely  influenced  by  the  size,  outlines,  and 
locations  of  the  continents  of  the  globe;  and  a  summary  inspec- 
tion of  a  magnetic  chart  of  the  globe  indicates  that  such  is 
actually  the  case. 

THE  AURORA. 

Let  us  now  consider  the  phenomena  produced  by  the  passage 
of  the  Earth  through  a  particular  one  of  the  streams  ejected 
from  the  Sun.  In  certain  longitudes,  at  a  given  instant  of  time, 
the  direction  of  the  stream  will  be  more  nearly  at  right  angles 
to  the  direction  of  the  Earth's  magnetic  lines  of  force  than  in 


By  J.  M.  Schaeberle.  53 

other  longitudes.  Now,  in  the  case  of  a  permanent  magnet, 
wound  by  a  coil  of  some  conducting  material  in  the  form  of  an 
insulated  wire,  an  electric  discharge  can  be  produced  between 
the  terminal  points  of  this  wire,  if  a  magnetic  body  is  moved 
rapidly  across  the  lines  of  force  of  the  magnet;  the  discharge 
will  take  place  along  the  line  of  least  resistance. .  Applying  this 
principle  to  the  case  of  the  Earth  and  the  stream,  then,  if  my 
reasoning  is  sound,  it  would  seem  to  follow  (1)  that  there  will 
be  a  tendency  for  a  discharge  to  take  place  between  the  particles 
of  the  stream,  and  that  (2)  such  a  discharge  will  be  in  the  direc- 
tion of  the  Earth's  magnetic  meridian;  since  each  individual 
particle  of  the  stream,  on  entering  the  Earth's  magnetic  field,  will 
at  once  take  such  a  position  that  the  line  joining  its  own  poles 
will  lie  in  the  direction  of  the  magnetic  meridian,  and  as  these 
same  particles  will  act  as  conductors,  the  lines  of  least  resist- 
ance will  be  formed  in  the  magnetic  meridians. 

If  we  take  it  for  granted  that  there  is  an  electrostatic  condi- 
tion in  which  a  positively  electrified  stratum  is  separated  from 
one  negatively  electrified  by  an  insulating  stratum  of  air,  then 
a  much  simpler  explanation  results.  The  lines  of  least  resist- 
ance will  be  formed  precisely  as  in  the  first  hypothesis;  these  lines 
joining  two  differently  charged  strata  will  evidently  be  shortest 
(and  the  discharges  therefore  most  brilliant)  at  the  magnetic 
poles,  while  near  the  equator  no  discharges  can  take  place,  since 
any  given  line  of  least  resistance  will  lie  wholly  within  a  given 
stratum.  The  intensity  of  the  discharge  will  decrease  as  the 
area  over  which  the  discharges  take  place  increases.  When 
the  number  of  discharges  is  very  great,  we  have  the  condition 
of  a  great  number  of  nearly  parallel  luminous  lines  more  or 
less  inclined  to  each  other,  so  that  in  addition  to  the  apparent 
motions  towards  the  magnetic  zenith,  concentric  arches  (rays) 
may  be  formed,  which  will  slowly  vary  with  variations  in  the 
arrangement  of  the  luminous  discharges.  (See  Plate  VIII., 
Figures  10  and  11,  inverted.  The  parallactic  effect  will  depend 
on  the  distance  of  the  display  from  the  observer,  so  that  the 
arches  (rays)  formed  may  be  either  convex  or  concave  in  per- 
spective.) Many  of  the  rapid  motions  may  be  only  apparent, 
and  due  to  an  actual  shifting  of  the  points  of  perspective 
intersection  of  continuous  discharges,  which  have  a  slight 
lateral  motion.  Figure  1,  Plate  VII.,  illustrates  the  low  auroral 


54        A  Mechanical  Theory  of  the  Solar  Corona, 


arch.  If  the  gratings  are  slightly  shifted,  this  luminous  arch 
can  be  changed  to  a  dark  segment.  Dark  segments  at  other  alti- 
tudes are  illustrated  in  Figures  10,  11,  125  and  13. 

Gravitational  and  atmospheric  disturbances  will  constantly 
tend  to  break  existing  conductors,  and  to  form  new  ones  so  long 
as  the  suspended  particles  are  sufficiently  numerous. 

To  further  test  this  theory,  the  following  conditions  should 
be  fulfilled: 

As  the  streams  ejected  from  the  Sun  have  the  greatest  density 
in  about  15°  heliocentric  latitude,  the  number  of  auroras 
should  be  greatest  in  the  months  corresponding  to  the  times 
when  the  heliocentric  latitude  ft  of  the  Earth  is  greatest,  and 
least  when  latitude  of  the  Earth  is  zero.  As,  however,  a  return- 
ing stream  is  more  likely  to  pass  near  the  Earth  than  an  out- 
going one  (on  account  of  the  tendency  of  the  outer  planets  to 
diminish  the  latitudes  of  all  the  streams),  the  pole  which  is 
turned  towards  a  returning  stream  when  the  Earth  is  in  the 
plane  of  the  Sun's  equator  will  have  more  decided  displays 
than  the  one  turned  towards  the  Sun.  The  Earth  is  in  the 
plane  of  the  Sun's  equator  in  June  and  December,  and  during 
the  latter  month  the  north  pole  attains  its  greatest  inclination 
away  from  the  Sun,  so  that  the  frequency  of  auroras  should  be 
more  decided  in  the  Northern  Hemisphere  in  December  than  in 
June;  the  effect  of  the  longer  nights  will  also  cause  an  apparently 
greater  number  of  displays  in  December.  The  Earth  attains  its 
greatest  heliocentric  latitudes  in  March  and  September,  and  both 
poles  are  equally  exposed  to  the  solar  influences  at  these  times, 
consequently  the  auroras  should  not  only  be  most  numerous  at 
these  times,  but  in  both  months  the  number  should  be  about 
the  same.  I  take  the  following  data  from  the  article  on  Meteor- 
ology, Vol.  XVI.  of  the  Encyclopaedia  Britannica: 

MONTHLY  FREQUENCY  OF  EUROPEAN  AURORAS. 


Jan. 

Feb. 

Mar. 

April. 

May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

229 

307 

440 

312 

184 

65 

87 

217 

405 

497 

285 

225 

If  a  series  of  observations  should  be  manufactured  to  fit  this 
theory,  the  above  figures  could  hardly  be  improved  upon. 


By  J.  M.  Schaeberle.  55 

I  have  not  been  able  to  find  a  series  of  observations  for  the 
Southern  Hemisphere.  It  at  once  follows  that  if  the  streams 
have  periods  of  maxima  and  minima  of  magnitude  and  fre- 
quency, the  auroras  will  have  similar  and  nearly  coincident 
periods,  the  returning  streams,  as  a  rule,  governing  the  magni- 
tude of  the  display;  although,  when  the  perturbations  of  the 
streams  near  the  Sun's  surface  are  greatest,  the  slightly  deflected 
outgoing  streams,  from  the  higher  latitudes,  will  be  more  apt  to 
cross  the  Earth's  path.  If  these  streams  are  composed  of  small 
particles,  the  auroral  phenomena  will  be  largely  confined  to  the 
higher  regions  of  the  Earth's  atmosphere.  (So  far  as  the  final 
precipitation  of  such  particles  to  the  Earth  is  concerned,  the 
prevailing  direction  of  the  upper  atmospheric  currents  will  have 
much  to  do  with  the  final  location  of  such  masses  on  the  Earth's 
surface,  and  here,  again,  the  tendency  will  be  to  carry  these 
masses  towards  the  poles,*if  our  present  views  on  the  currents 
of  the  upper  atmosphere  are  correct.) 

The  monthly  variation  in  auroral  frequency  is  thus  accounted 
for.  The  variation  in  the  absolute  numbers  of  the  auroras,  tak- 
ing the  whole  world  together,  will  depend  upon  the  number  of 
the  streams,  and  will,  therefore,  pass  through  a  cycle  every  ten 
or  eleven  years,  precisely  as  the  Sun  spots  do,  according  to  the 
theory,  and  in  fact. 

VARIABLE  AND  NEBULOUS  STARS. 

It  seems  to  me  that  many  of  the  irregular  variations  in  the 
physical  appearances  of  certain  classes  of  stars  can  be  satis- 
factorily explained  by  the  theory  of  ejected  streams  colliding 
at  certain  intervals  with  the  returning  ones.  Viewed  from 
great  distances  such  stars  would  appear  to  be  surrounded  by 
nebulous  envelopes  of  varying  brightness,  and  according  to  the 
position  of  the  axis  of  rotation  and  the  zones  of  maximum 
activity  with  reference  to  the  line  of  sight  the  nebulosity 
would  appear  to  be  either  circular  or  more  or  less  elliptical  in 
outline.  The  bearing  of  this  theory  on  Professor  LOCKYER'S 
Meteoritic  Hypothesis  is  significant  (so  far  as  I  can  learn  from 
mere  notices  of  his  work"  just  issued),  since  these  results  have 
been  obtained  without  any  preconceived  notions  as  to  whether 
the  explanation  of  certain  phenomena  would  agree  or  disagree 
with  any  other  theory. 


56        A  Mechanical  Theory  of  the  Solar  Corona. 

COMETS. 

The  hypothesis,  favored  by  some  astronomers,  that  the  matter 
now  revolving  about  the  Sun,  in  cometary  orbits,  was  once 
ejected  from  the  Sun,  is,  according  to  the  Mechanical  Theory, 
rendered  extremely  probable,  and  it  would  not  be  difficult  to 
bring  forward  many  strong  arguments  to  support  this  view  and 
to  account  for  many  apparent  changes  of  form  in  cometary 
matter.  But  the  length  of  this  postscript  has  already  far 
exceeded  my  original  intentions,  and  I  now  await  the  result  of 
the  final  verdict  as  to  the  merits  of  my  investigations,  to  be 
given  by  those  who  are  most  competent  to  pass  judgment. 


Photomount 
Pamphlet 

Binder 
Gaylord  Bros. 

Makers 
Stockton,  Calif. 

PAT.  JAN.  21.  1908 


"36351 

0.652? 


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